Hi,
I once had to strip a 12ft tall oak mantel/overmantel. It had the works in terms of carving and trim, including dentils. I carefully removed the strip of moulding that had the dentils cut into it, and immersed it in a trough (a section of half-round gutter works well for this) of stripper 'til the sides of the dentils were clean. I was able to use a sharpened putty knife to clean up those end-grain edges pretty well. Then the mldg can be sanded before being reinstalled.
If the wood is stained with a dark un-removable deep red color, it probably isn't cherry, but birch stained to resemble mahogany. This was terribly popular in the first couple of decades of the last century for architectural woodwork. The stain is an aniline dye, and will bleed through some kinds (many kinds) of paint. An antidote if you want to tone down the red is to overlay a coat of a greenish stain; minwax black walnut stain is good for this. The end result is a warm deep brown.
Casey

Thanks for the suggestion. Unfortunately the only parts that can be removed are the pediment and the drawers (3 of them). Since this was a built-in cabinet , it is 19 in deep, we can see the sides clearly and it is definitly solid cherry. I tried sanding the back of the pediment to see how much of the stain can be removed and it will work to get a lot of it off as it has not penetrated the wood very far. So ....hours and hours and hours....email me if you want to come and help !!! Thanks for the color suggestion. We have old oak hardwood floors in that area of the house and will want something that goes with that.

Look for a stripper that contains Methylene Chloride.
Be very careful it is rather nasty stuff.
Use it outdoors.
Do not use it if you have any history of heart problems.
It ties up blood hemoglobin just like CO.
For a healthy person outdoors it is safe.

A real paint store is more likely to have it than the big box.

It was also suggested that I try to find 5F5....is that the same as Methylene Chloride ? I am in WAY over my head with this. I can now see a tiny dot on each dentil piece where it was nailed on. There is a 6 foot run of this stuff !!! I will see about immersing the pediment and the drawer fronts...very good idea. I wish the stripper was not so expensive. THANKS for the help.

I cannot tell since there is not an MSDS sheet around.
If it contains Methylene Chloride it will list it on the can.