You can try various solvents depending on what the type of paint is.
Latex comes off with various cleaners (409 type) if the surface prep was less than perfect. Xylene and denatured alcohol are also effective but should be tested to make sure they will not damage the underlying finish.
If the paint is oil based (alkyd) you are very likely to have to refinish by the time you strip it off.
Carefully removing the woodwork and stripping it in the basement or garage and then refinishing is another option.

Depending on what the finish was before the paint you might be able to break the bond using a steam cleaner. First I would check the finish on the unpainted portions of the door to determine if it's varnish (solvent for that is mineral spirits or turps) or shellac (solvent for that is alcohol). If the wood-colored parts are covered with varnish I think you'll have an easier time breaking the bond. Shellac might be harmed by the steam. And maybe you'll get lucky and have varnish topped with latex paint. That's the easiest pairing to crack.

However, depending on how old your house is the wood grain "takes your breath away" may be faux graining, not the actual wood pattern. In my c. 1840 NY house much of my woodwork had this treatment, and has since been painted. I can see where it was done, perhaps as practice, on the back sides of doors. Grain painting present special challenges as the graining may have been done with one medium, then topped by another to protect, maybe not. In historic restoration projects I have read of successful cleaning and restoration of faux grain painting, but I imagine it's very fussy work.

And just as aside to anyone playing around with alcohol solvents. I recently acquired several liters of grain alcohol to use in cleaning books and have experimented with it on shellac-finished furniture and been amazed at how easy it is to work with compared to denatured alcohol. I think it is higher proof, so perhaps a more ready solvent. It's not cheap, and hard to find - and may be illegal in some states, but it's worth looking into. I live in NY, and can't buy it here, so I go to Vermont and special-order it at State Liquor Stores. You have to fill out several forms and sign an affadavit that it's not for human consumption (only for scientific, educational or research purposes). I just stated I was using it for cleaning books and antiques and the form came back approved along with my order of the stuff. The clerk in the liquor store said they had had to remove if from sale because college kids were using it to create something called Jello-shots, which sound vile. I don't think that's quite what the intended educational use is, though!

Molly~

Thanks so much to both of you. I guess I'll have to wait until it's "ours" to develop a game plan for this. Your input's very helpful.

I'm pretty sure it's not painted grain, but I'll take a closer second look next time we're there.

Thanks!!

Kim