The answer
It can. A transaction spending several inputs may trigger a common-input-ownership heuristic, linking addresses that previously looked separate. Certain collaborative transactions complicate this heuristic.
What to do next
Consider coin-selection privacy implications before consolidation; do not assume new receive addresses protect earlier links.
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Frequently asked questions
Does this prove every combined input had one owner?
No. Heuristics are probabilistic, and collaborative protocols can combine inputs from different owners.