As of now, you can only do this when using tutor dev. In a normal production tutor local launch, only the MFE build artifacts are copied into the single mfe image, and there’s no way to individually mount directories from the local filesystem. This is intentional, though: there’d be little reason to use containers, otherwise.
That said, we (as in, the Open edX community) are well aware of these and other related frontend issues, and are working on trying to solve them. If you’re interested, you can check out my last conference talk, which presents one of the prongs we’re attacking the problem with (essentially, rendering the page frame, including the header, outside MFEs).
For the other (known) prongs, checkout this PR to add loading external CSS themes, and the Design Tokens ADR.