Maybe? Soyuz is too cramped, but Dragon might be able to fit extra people. A few years ago a NASA astronaut flew up on a leaky Soyuz, so they looked at using Dragon as a lifeboat:
Dragon was drawn up to fit 7 people, with 3 seats on the bottom and 4 on top. They ended up changing the seat angles for reentry, so now they only have 4.
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Starliner is still their emergency ride home in case a real alarm goes off, but they want to study the leak issue as much as possible before they separate their service module, which burns up during reentry.
The docking adapters look pretty much the same (interlocking petals, not male/female) and can be active, passive, or both, but Dragon's is only active. Active has to dock to passive, so two Dragons couldn't dock.
SpaceX developed a new one that can be active or passive for Starship, which will have to dock with Orion and the Lunar Gateway.