The expensive part of every Legendre stage is generating the associated Legendre values on the fly by recurrence -- work that depends only on (m, theta), never on the field. Batched kernels walk the recurrence once for up to 4 fields, one accumulator lane each, with per-lane arithmetic textually identical to the scalar kernels': batched and scalar plans produce bit-identical states. synth/analys now take multiple fields -- [a, b] = synth(x, y) -- as explicit grouping: output k is the transform of input k, and the planner (materializeTransforms) chunks each group into whatever lane width the device supports. The lanes' fm scratch lives in one 256-aligned arena buffer, so the batched bind group is 3 tables + K fields + 1 arena = 8, exactly WebGPU's default storage-buffer limit at K = 4 -- full-width batching on every stack, SwiftShader included. Ungrouped transforms on consecutive independent lines batch the same way; SHT_BATCH=0 compiles scalar-only plans for A/B. The models group their solve-loop transforms across species (all 16 transforms of a schnakenberg step land in batches) and their init pairs. Misuse is refused at compile time: a group must bind every output, since each input costs a transform. Worth ~25% of the whole step: 0.88 vs 1.14 ms/step at lmax 127, niter 2, on bumpy -- 2.22 -> 0.88 ms cumulative with the flux-form reduction. Needs numbl >= 6035240 ("Route .mtoc2.js user functions through builtin multi-assign") for the multi-output external lowering; bump NUMBL_REF in .github/workflows when that lands.