Querying across heterogeneous data models incurs overhead from query decomposition, result retrieval and conversion, and processing outside the underlying database systems. This paper investigates the extent to which, in a decomposition-based architecture, this cross-model tax results from decisions made by the unifying query processor rather than from heterogeneity alone. We present a mapping- and capability-aware optimization approach that moves applicable processing into native query parts. It combines model-aware predicate pushdown, cross-model dependent joins, and non-redundant query-part construction within a unified pipeline spanning relational, document, and graph databases. The approach is implemented in MM-quecat and evaluated using 20 read-only queries across PostgreSQL, MongoDB, and Neo4j, as well as a heterogeneous combination of the three systems in a single-machine, containerized deployment. For the query--environment combinations most affected by large intermediate results, predicate pushdown yields maximum observed latency reductions of up to two orders of magnitude and prevents the out-of-memory failures observed in the original single-DBMS experiments. Dependent execution further improves eligible external joins, while non-redundant construction reduces planning time for the largest evaluated graph plans, from hundreds of milliseconds to several milliseconds. The results show how established optimization principles can be applied across conceptual, mapping, data-model, and DBMS boundaries in decomposition-based multi-model query processing.

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