Depends on how gentle you are. If yous tain it darker you will lose a lot of the detail....contrast. But.
I would remove the finish with something like a furniture restorer....or make a mix of shellac thinner and lacquer thinner....3 parts shellac thinner to 1 part lacquer thinner. wipe it on, let it sit for a minute and wipe off with a soft cloth.
Because there will still be some finish left, I would thn apply a gel stain or even a tinted varnish.
Do all the above outside and wear gloves......dangerous chemicals!!
Linda C

thank you for the response, Linda.....actually toning down the contrast is something I wanted to do....the piece (it has a set of chairs that go with it) is a bit ornate looking for my taste, and I thought toning down the contrast might give it a more subtle appearance....the part of the table I worry the most about staining is the 'burled' wood inlay around the circumference ...I guess I am worried that one type of wood finish will take the stain too differently from the other, therefore negating my desired intent

Here is a link that might be useful: Chairs pictured here

Unless you completely clean the finish off of the table, it won't "take" the stain...any stain you put on will just lie on top of the remaining finish/sealer.
That's why I recommended a gel stain or a tinted varnish.