diff --git a/Cargo.lock b/Cargo.lock
index b895c02..e49342a 100644
--- a/Cargo.lock
+++ b/Cargo.lock
@@ -125,14 +125,14 @@ dependencies = [
 
 [[package]]
 name = "ironnest"
-version = "0.4.0"
+version = "0.4.1"
 dependencies = [
  "ironnest-optimizer",
 ]
 
 [[package]]
 name = "ironnest-cde"
-version = "0.4.0"
+version = "0.4.1"
 dependencies = [
  "anyhow",
  "float-cmp",
@@ -145,7 +145,7 @@ dependencies = [
 
 [[package]]
 name = "ironnest-geo"
-version = "0.4.0"
+version = "0.4.1"
 dependencies = [
  "anyhow",
  "float-cmp",
@@ -161,7 +161,7 @@ dependencies = [
 
 [[package]]
 name = "ironnest-optimizer"
-version = "0.4.0"
+version = "0.4.1"
 dependencies = [
  "insta",
  "ironnest-cde",
@@ -171,7 +171,7 @@ dependencies = [
 
 [[package]]
 name = "ironnest-py"
-version = "0.4.0"
+version = "0.4.1"
 dependencies = [
  "ironnest",
  "pyo3",
diff --git a/Cargo.toml b/Cargo.toml
index a2a9965..0209946 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -5,7 +5,7 @@ resolver = "3"
 members  = ["crates/geo", "crates/cde", "crates/optimizer", "crates/ironnest", "crates/py"]
 
 [workspace.package]
-version      = "0.4.0"      # bump deliberately; re-bless goldens if placement code changed
+version      = "0.4.1"      # bump deliberately; re-bless goldens if placement code changed
 edition      = "2024"       # jagua-rs lineage; edition 2024 needs Rust ≥ 1.85
 rust-version = "1.87"       # MSRV floor: jagua's forked code uses {integer}::cast_signed/cast_unsigned
                             # (stable 1.87). We build on the pinned 1.96.0 — see rust-toolchain.toml.
diff --git a/crates/ironnest/src/lib.rs b/crates/ironnest/src/lib.rs
index 3760a05..579ac22 100644
--- a/crates/ironnest/src/lib.rs
+++ b/crates/ironnest/src/lib.rs
@@ -20,5 +20,6 @@
 #[doc(inline)]
 pub use ironnest_optimizer::{
     MultiSheetSolution, NestSolution, Placement, Scalar, Sheet, nest, nest_multi,
-    nest_multi_per_item, nest_multistart, nest_multistart_per_item, nest_per_item,
+    nest_multi_multistart, nest_multi_multistart_per_item, nest_multi_per_item, nest_multistart,
+    nest_multistart_per_item, nest_per_item,
 };
diff --git a/crates/optimizer/src/lib.rs b/crates/optimizer/src/lib.rs
index 525ced9..d223ff1 100644
--- a/crates/optimizer/src/lib.rs
+++ b/crates/optimizer/src/lib.rs
@@ -607,10 +607,49 @@ pub fn nest_multi(
     seed: u64,
     budget: u64,
 ) -> MultiSheetSolution {
-    // Broadcast the single rotation set to every item, then run the per-item path (byte-identical —
-    // see [`nest`]).
+    nest_multi_multistart(items, qty, sheets, min_sep, rotations_deg, seed, budget, 1)
+}
+
+/// Like [`nest_multi`], but with a **distinct allowed-rotation set per item type** — `rotations_deg[k]`
+/// applies to `items[k]` (`rotations_deg.len() == items.len()`). Carries the per-item semantics of
+/// [`nest_per_item`] across the multi-sheet spill. Same determinism contract as [`nest_multi`].
+#[must_use]
+#[allow(clippy::too_many_arguments)]
+pub fn nest_multi_per_item(
+    items: &[Vec<[Scalar; 2]>],
+    qty: &[usize],
+    sheets: &[Sheet],
+    min_sep: Scalar,
+    rotations_deg: &[Vec<Scalar>],
+    seed: u64,
+    budget: u64,
+) -> MultiSheetSolution {
+    nest_multi_multistart_per_item(items, qty, sheets, min_sep, rotations_deg, seed, budget, 1)
+}
+
+/// [`nest_multi`] with **deterministic best-of-K multi-start applied to every sheet**: each sheet is
+/// packed with the densest of `n_starts` decorrelated-seed runs *before* the leftover demand spills to
+/// the next. Maximising each sheet's fill directly reduces what spills forward, so fewer sheets / less
+/// material are used on a mixed-parts job. Applies **one** rotation set to every item; for a per-item
+/// set use [`nest_multi_multistart_per_item`].
+///
+/// `n_starts` is clamped to ≥ 1; **`n_starts == 1` is byte-identical to [`nest_multi`]**, so existing
+/// behaviour is unchanged. Same determinism contract — the per-sheet best-of-K is byte-deterministic
+/// (see [`nest_multistart`]); under the `parallel` feature each sheet's K starts run on threads.
+#[must_use]
+#[allow(clippy::too_many_arguments)]
+pub fn nest_multi_multistart(
+    items: &[Vec<[Scalar; 2]>],
+    qty: &[usize],
+    sheets: &[Sheet],
+    min_sep: Scalar,
+    rotations_deg: &[Scalar],
+    seed: u64,
+    budget: u64,
+    n_starts: usize,
+) -> MultiSheetSolution {
     let rotations_per_item = vec![rotations_deg.to_vec(); items.len()];
-    nest_multi_per_item(
+    nest_multi_multistart_per_item(
         items,
         qty,
         sheets,
@@ -618,15 +657,16 @@ pub fn nest_multi(
         &rotations_per_item,
         seed,
         budget,
+        n_starts,
     )
 }
 
-/// Like [`nest_multi`], but with a **distinct allowed-rotation set per item type** — `rotations_deg[k]`
-/// applies to `items[k]` (`rotations_deg.len() == items.len()`). Carries the per-item semantics of
-/// [`nest_per_item`] across the multi-sheet spill. Same determinism contract as [`nest_multi`].
+/// [`nest_multi_multistart`] with a **distinct allowed-rotation set per item type** (the
+/// [`nest_per_item`] semantics). Each sheet runs a best-of-`n_starts` pack against the remaining
+/// demand; `n_starts == 1` reduces to [`nest_multi_per_item`] byte-for-byte.
 #[must_use]
 #[allow(clippy::too_many_arguments)]
-pub fn nest_multi_per_item(
+pub fn nest_multi_multistart_per_item(
     items: &[Vec<[Scalar; 2]>],
     qty: &[usize],
     sheets: &[Sheet],
@@ -634,6 +674,7 @@ pub fn nest_multi_per_item(
     rotations_deg: &[Vec<Scalar>],
     seed: u64,
     budget: u64,
+    n_starts: usize,
 ) -> MultiSheetSolution {
     assert_eq!(
         items.len(),
@@ -651,9 +692,11 @@ pub fn nest_multi_per_item(
 
     for (i, sheet) in sheets.iter().enumerate() {
         // A distinct, deterministic per-sheet seed (SplitMix64 in the PRNG de-correlates adjacent
-        // seeds, so `seed + i` gives well-separated streams).
+        // seeds, so `seed + i` gives well-separated streams). Each sheet's K best-of-K runs then
+        // derive from that seed (`sheet_seed + k`); the K runs of a given sheet are decorrelated from
+        // each other — the property best-of-K relies on — independent of the cross-sheet stride.
         let sheet_seed = seed.wrapping_add(i as u64);
-        let sol = nest_per_item(
+        let sol = nest_multistart_per_item(
             items,
             &remaining,
             &sheet.outline,
@@ -662,6 +705,7 @@ pub fn nest_multi_per_item(
             rotations_deg,
             sheet_seed,
             budget,
+            n_starts,
         );
 
         for p in &sol.placements {
diff --git a/crates/optimizer/tests/nest.rs b/crates/optimizer/tests/nest.rs
index 6a3d499..c63664a 100644
--- a/crates/optimizer/tests/nest.rs
+++ b/crates/optimizer/tests/nest.rs
@@ -7,8 +7,8 @@
 //! byte-identical placements).
 
 use ironnest_optimizer::{
-    Scalar, Sheet, nest, nest_multi, nest_multi_per_item, nest_multistart,
-    nest_multistart_per_item, nest_per_item,
+    Scalar, Sheet, nest, nest_multi, nest_multi_multistart, nest_multi_multistart_per_item,
+    nest_multi_per_item, nest_multistart, nest_multistart_per_item, nest_per_item,
 };
 
 /// An axis-aligned `w × h` rectangle with its lower-left corner at the origin (CCW).
@@ -675,6 +675,90 @@ fn multi_sheet_demand_exceeding_capacity_no_underflow() {
     assert_eq!(sol.unplaced.len(), 9);
 }
 
+// ---------------------------------------------------------------------------
+// Multi-sheet multi-start (best-of-K per sheet)
+// ---------------------------------------------------------------------------
+
+#[test]
+fn multi_sheet_multistart_k1_is_byte_identical_to_nest_multi() {
+    // restarts=1 must equal nest_multi bit-for-bit (keeps the existing multi-sheet behaviour) — the
+    // same load-bearing invariant the single-sheet path holds.
+    let items = vec![rect(10.0, 10.0)];
+    let sheets = vec![
+        Sheet {
+            outline: rect(35.0, 35.0),
+            holes: vec![],
+        },
+        Sheet {
+            outline: rect(35.0, 35.0),
+            holes: vec![],
+        },
+    ];
+    let single = nest_multi(&items, &[16], &sheets, 0.0, &CARDINAL, 9, 1200);
+    let multi = nest_multi_multistart(&items, &[16], &sheets, 0.0, &CARDINAL, 9, 1200, 1);
+    assert_eq!(single, multi, "restarts=1 must equal nest_multi");
+    // n_starts=0 clamps to 1.
+    let zero = nest_multi_multistart(&items, &[16], &sheets, 0.0, &CARDINAL, 9, 1200, 0);
+    assert_eq!(single, zero, "restarts=0 clamps to a single start");
+}
+
+#[test]
+fn multi_sheet_multistart_is_deterministic_and_broadcast_matches() {
+    let items = vec![rect(13.0, 7.0)];
+    let sheets = vec![
+        Sheet {
+            outline: rect(50.0, 50.0),
+            holes: vec![],
+        },
+        Sheet {
+            outline: rect(50.0, 50.0),
+            holes: vec![],
+        },
+    ];
+    let a = nest_multi_multistart(&items, &[40], &sheets, 0.0, &CARDINAL, 1, 1000, 3);
+    let b = nest_multi_multistart(&items, &[40], &sheets, 0.0, &CARDINAL, 1, 1000, 3);
+    assert_eq!(
+        a, b,
+        "multi-sheet best-of-K must be byte-identical for the same args"
+    );
+    let broadcast = vec![CARDINAL.to_vec()];
+    let per_item =
+        nest_multi_multistart_per_item(&items, &[40], &sheets, 0.0, &broadcast, 1, 1000, 3);
+    assert_eq!(
+        a, per_item,
+        "broadcast per-item multi-sheet multistart must equal uniform"
+    );
+}
+
+#[test]
+fn multi_sheet_multistart_never_places_fewer_than_single() {
+    // Homogeneous parts ⇒ each sheet's best-of-K places ≥ the single start on the same remaining, and
+    // the greedy spill carries that forward (a denser earlier sheet leaves at most that many fewer for
+    // the next), so the total placed can never drop below the single-start total.
+    let items = vec![rect(13.0, 7.0)];
+    let sheets = vec![
+        Sheet {
+            outline: rect(50.0, 50.0),
+            holes: vec![],
+        },
+        Sheet {
+            outline: rect(50.0, 50.0),
+            holes: vec![],
+        },
+    ];
+    let placed = |s: &ironnest_optimizer::MultiSheetSolution| -> usize {
+        s.per_sheet.iter().map(Vec::len).sum()
+    };
+    let single = nest_multi(&items, &[40], &sheets, 0.0, &CARDINAL, 1, 1000);
+    let multi = nest_multi_multistart(&items, &[40], &sheets, 0.0, &CARDINAL, 1, 1000, 4);
+    assert!(
+        placed(&multi) >= placed(&single),
+        "best-of-4 multi-sheet ({}) must place at least the single start ({})",
+        placed(&multi),
+        placed(&single),
+    );
+}
+
 // ---------------------------------------------------------------------------
 // Collision-footprint decimation for high-vertex curved parts
 //
diff --git a/crates/py/src/lib.rs b/crates/py/src/lib.rs
index f95759e..dc5180b 100644
--- a/crates/py/src/lib.rs
+++ b/crates/py/src/lib.rs
@@ -12,8 +12,9 @@
 //! byte-identical, cross-platform-reproducible output (proven by the Phase-3 golden).
 
 use ironnest_core::{
-    Sheet, nest_multi_per_item as nest_multi_impl,
-    nest_multistart_per_item as nest_multistart_impl, nest_per_item as nest_impl,
+    Sheet, nest_multi_multistart_per_item as nest_multi_multistart_impl,
+    nest_multi_per_item as nest_multi_impl, nest_multistart_per_item as nest_multistart_impl,
+    nest_per_item as nest_impl,
 };
 use pyo3::exceptions::PyValueError;
 use pyo3::prelude::*;
@@ -246,6 +247,11 @@ fn nest(
 ///     identically.
 /// sheets : list[tuple[list[tuple[float, float]], list[list[tuple[float, float]]]]]
 ///     Each sheet is ``(outline, holes)`` — a boundary outline plus its keep-out holes.
+/// restarts : int, optional
+///     Best-of-K multi-start applied **per sheet** (default ``1`` = byte-identical to the historical
+///     behaviour). Each sheet is packed with the densest of ``restarts`` decorrelated-seed runs before
+///     leftover demand spills to the next, so fewer sheets / less material are used on a mixed-parts
+///     job. Same determinism contract; the K runs of each sheet execute in parallel (GIL released).
 ///
 /// Returns
 /// -------
@@ -256,7 +262,7 @@ fn nest(
 /// Each sheet is nested with a seed derived deterministically from `seed`, so the result is
 /// byte-identical for the same arguments.
 #[pyfunction]
-#[pyo3(signature = (items, qty, sheets, min_sep, rotations, seed, budget))]
+#[pyo3(signature = (items, qty, sheets, min_sep, rotations, seed, budget, restarts=1))]
 #[allow(clippy::needless_pass_by_value)]
 #[allow(clippy::too_many_arguments)] // `py` is the injected GIL token (not an oracle input); the rest are the oracle's input surface
 fn nest_multi(
@@ -268,6 +274,7 @@ fn nest_multi(
     rotations: Bound<'_, PyAny>,
     seed: u64,
     budget: u64,
+    restarts: usize,
 ) -> PyResult<(Vec<Vec<PyPlacement>>, Vec<usize>)> {
     if items.len() != qty.len() {
         return Err(PyValueError::new_err(format!(
@@ -287,8 +294,17 @@ fn nest_multi(
         .collect();
 
     // Release the GIL for the solve — see the note in `nest` for the why and the safety argument.
-    let solution =
-        py.detach(|| nest_multi_impl(&items, &qty, &sheets, min_sep, &rotations, seed, budget));
+    // `restarts <= 1` is the historical single-start spill; `> 1` packs each sheet best-of-K. Both
+    // honour the determinism contract.
+    let solution = py.detach(|| {
+        if restarts <= 1 {
+            nest_multi_impl(&items, &qty, &sheets, min_sep, &rotations, seed, budget)
+        } else {
+            nest_multi_multistart_impl(
+                &items, &qty, &sheets, min_sep, &rotations, seed, budget, restarts,
+            )
+        }
+    });
 
     let per_sheet = solution
         .per_sheet