Stain over patches of old stain

Hey all. I'm a woodworking newbie, so bear with me.
I'm working on a 15-year old desk. I took it apart, zip-stripped, then sanded. There are still patches of old stain, however, in some areas. I've tried repeating zip-stripping and sanding, but those few areas won't come off. I'm sure a master woodworker could probably get them off, but I don't want to ruin the wood.
Question: can I stain over this old stain? Is it like paint, where a few coats will cover up blemishes? I've started staining another area of the desk (one that was completely stripped) with a dark finish, and it looks great. Will a couple of coats and then a clearcoat do the job?
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Probably
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Mike G.
Heirloom Woods
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