Click-through rate (CTR) models vary in feature-interaction design, yet their top networks usually remain a single multilayer perceptron shared by all examples. Heterogeneous user, item, and context subgroups therefore update the same parameters; weakly aligned learning signals make the aggregate gradient a compromise among competing directions. We study the competition on Avazu with 4 models and 4 semantic fields. Across all architectures, semantic subgroups show lower Top-NN gradient cosine similarity than random groups matched by sample size and label ratio, with reductions of 0.23-0.37. This competition motivates input-conditioned experts, but directly replacing an established Dense mapping changes its initial function, sharing pattern, and capacity, obscuring the source of gains. We introduce PRIME (Plug-in Residual Input-conditioned Mixture of Experts), a Dense-anchored mixture of low-rank residual experts. PRIME anchors the original prediction and uses zero-residual initialization to match the Dense baseline exactly at training onset. Input-dependent routing weights low-rank experts for example-specific logit corrections; multi-bag aggregation and EMA load biases stabilize conditional estimation. We evaluate PRIME on held-out Avazu and Criteo test sets across 13 CTR architectures and five paired seeds. Median paired AUC gains are +0.0022 and +0.0066, with LogLoss reductions of 0.0011 and 0.0081, respectively. On FiBiNET and DCNv2, PRIME outperforms APG in all ten seed-level AUC comparisons while using fewer parameters and lower inference latency on both backbones. These results show that function-preserving conditional residuals add input-dependent capacity while preserving the Dense path and its optimization stability. Code is available at https://github.com/YH-learning/PRIME.

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