Staining various woods in trim project to look "similar"
I'm planning on doing some wainscotting in a newly finished basement. To save a lot on wood costs and seasonal movement of the wood, I plan on making the stiles and rails out of 3/4 birch ply, a flat panel of 1/4 ply then trim the panel with poplar bolection moulding bought from a lumber yard. Also a cap made from poplar and base moulding from the same. I also plan to order doors in poplar. SO, my question is, is it a pipe dream to think I can stain/color birch and poplar to appear (to the average person) to look the same? I would like to go with a darker color, possibly like dark cherry or mahogany. I realize the differences in grain patters cannot be altered. As far as equipment, I just bought an earlex 5500 but have not run stain through it yet. Happy festivus everyone!