Approximation is a technique that optimizes the balance between application outcome quality and its resource usage. Trading quality for performance has been investigated for single application scenarios, but not for environments where multiple approximate applications may run concurrently on the same machine, interfering with each other by sharing machine resources. Applying existing, single application techniques to this multi-programming environment may lead to configuration space size explosion, or result in poor overall application quality outcomes. Our new RAPID-M system is the first cross-application con-figuration management framework. It reduces the problem size by clustering configurations of individual applications into local"similarity buckets". The global cross-applications configuration selection is based on these local bucket spaces. RAPID-M dynamically assigns buckets to applications such that overall quality is maximized while respecting individual application cost budgets.Once assigned a bucket, reconfigurations within buckets may be performed locally with minimal impact on global selections. Experimental results using six configurable applications show that even large configuration spaces of complex applications can be clustered into a small number of buckets, resulting in search space size reductions of up to 9 orders of magnitude for our six applications. RAPID-M constructs performance cost models with an average prediction error of ≤3%. For our application execution traces, RAPID-M dynamically selects configurations that lower the budget violation rate by 33.9% with an average budget exceeding rate of 6.6% as compared to other possible approaches. RAPID-M successfully finishes 22.75% more executions which translates to a 1.52X global output quality increase under high system loads. Theo verhead ofRAPID-Mis within≤1% of application execution times.