Multi-talker automatic speech recognition (MT-ASR) remains challenging in the presence of overlapping speech. Hard segmentation introduces irreversible errors, whereas serialized output training (SOT) avoids explicit segmentation but does not condition a pretrained encoder on speaker activity. We propose Soft Posterior Speaker Injection (SPSI). A Soft Posterior Head predicts per-frame speaker posteriors $\hat{\mathbf{P}}$ and injects them into Whisper through Multi-layer Feature-wise Linear Modulation (MFLM) and Speaker Memory Prompts (SMP). The benefit of SPSI concentrates where overlap is hardest and under domain transfer. On controlled two-speaker LibriSpeech overlap, SPSI reduces concatenated minimum-permutation word error rate (cpWER) from $61.5\%$ to $60.0\%$ in the high-overlap bin, with a smaller $51.9\%$ to $51.0\%$ change on the full set relative to SOT. Same-backbone speaker-auxiliary objectives and voice activity detection (VAD) pipelines do not outperform SOT. Zero-shot LibriCSS is comparable, but freeze-posterior overlap-heavy adaptation reduces held-out LibriCSS cpWER from $42.3\%$ to $36.8\%$ on sessions $8$--$9$, a $5.5$-point gain over SOT. Ablations indicate complementary roles of MFLM and SMP.

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