This assumes that the coordinator isn't analyzing the blockchain. It's plausible that the coordinator is fully aware of the inputs belonging to Alice, Bob, and Charlie.
What if her additional inputs aren't denied access? What if the coordinator has scrutinized her and can identify which of the requested coins belong to her? What if the coordinator declines to coinjoin any other input? Wouldn't that expose her anonymity without her knowledge?
In this incredibly far fetched scenario, then Alice and ask Bob or Charlie to verify they are able to join the same round.