Is it possible to set up a relationship between two fields that allows you to narrow choices.

I haven't had experience with it, but was also looking into this possibility of Conditional Dropdowns this morning actually.  It looks like this can be done only through a reference field from a relational table.  So if you were to create a separate table for those multiple choice fields and join it to the table you are looking to add this to, then you might be able to get it to work.

https://help.quickbase.com/user-assistance/conditional_dropdowns.html

This link helps explain it a bit more.