Federated learning (FL) must serve devices with varying computational capabilities. A fixed model cannot suit all devices, while training one model per deployment limit is costly. Federated supernet training instead learns one elastic model with differently sized subnetworks, then deploys a suitable one to each device. When client inference budgets differ, however, parameters exclusive to high-cost subnetworks are reachable by fewer clients. We propose FEAST, a federated shared-space training framework that counters this imbalance by jointly training multiple subnetworks within each client's limit. Budget-tailored sub-supernet routing sends only the relevant supernet portion, and sparse aggregation merges the returned parameter slices. The trained supernet directly serves the subnetworks used during federation and supports post-hoc extraction of additional subnetworks without federated retraining. We further show that independently assigning clients' training-data volumes and inference budgets can distort accuracy--inference-cost comparisons in heterogeneous FL simulations, and introduce a one-parameter $γ$-allocation protocol to control this coupling. In our experimental setup, the SuperFedNAS and DeepFedNAS supernet training procedures remain near chance at 25M and reach at most $17.09\%$ at $596$M inference MACs; FEAST reaches $71.06\%$ at $596$M, $2.4$ points above the strongest model-heterogeneous weight-sharing baseline at its largest tier. Across CIFAR-100, CINIC-10, and TinyImageNet-200, FEAST achieves the highest population-averaged accuracy among the evaluated weight-sharing methods when each client receives its largest affordable subnetwork. Sub-supernet routing reduces aggregate model-parameter traffic by $6.8\times$ relative to full-supernet transmission.
Heterogeneous Large Language Model (LLM) systems increasingly rely on shared contexts, retrieved evidence, and multi-agent dialogue histories, yet their internal key-value (KV) caches remain model-specific and cannot be reused across architectures. Consequently, each model must repeatedly prefill or store caches for the same context, limiting the scalability of multi-model reasoning and long-context generation. We propose Mixture-of-Translators(MoT), a cache translation framework that maps context KV caches from a source LLM into the cache space of a target LLM. Unlike prior approaches that depend on a single projection path or global shared latent space, MoT uses multiple translator modules to capture diverse source--target mappings. To further reduce residual translation error, we introduce a Context Correction Loss that aligns the replayed target trajectory with the native target trajectory. We reveal two competing failure modes in cache translation: propagated translation shift from early injection and last-state shift from late injection. MoT addresses them through translator mixtures and target-side correction. Across homogeneous and heterogeneous translations among Qwen2.5, GPT-2, and OPT models, MoT preserves downstream QA performance, including Qwen2.5-7B-scale translation with 51.0% average closed-set QA accuracy and 0.43 average extractive QA F1. In practical case studies, MoT enables quality-preserving memory reuse for multi-agent reasoning and retains 96.3% of direct-context quality in long-context cache-augmented generation, demonstrating scalable KV cache reuse across heterogeneous LLMs.