They usually can. In fact, before I listed the home in which I was living before I married and moved here, I actually removed a unit and brought it with me. I have seen built-ins where the sides and shelving were essentially freestanding and only minimally connected to the back of the unit, and that was majorly connected to the wall behind it. The unit would have had to have been completely disassembled and rebuilt in that case. It can be done, but at what amount of effort?

Also if you are considering removing the interior wall, scope out first to see if major bits of functioning lines are located in it (sometimes the case because the built-in sits back into unused space where those lines are hidden. I'm thinking sewer lines from an upstairs bath, water lines, furnace ducts. You really should know this before you start ripping. You may or may not be able to move these to a different location easily. Seen that happen!

Also determine if the wall you are ripping is load-bearing. You can sometimes work around that, with beams, but it adds costs and effort too. My husband did it with the wall between kitchen and dining room and it was a very good choice and he got lucky.

jajajo-
I don't want to be too negative here, but it all depends on how it was originally constructed. Specifically, was it a unit built off-site and then trimmed out in place, or was it built piece-by-piece as the house was assembled? If it's the latter, there may be a whole lot of disassembly involved and some of the parts ould get damaged. It would really help to post a picture. If you are going to proceed, consult a professional, like a finish carpenter, to get an assessment of the situation. Good luck.

I agree with kudzu 100%. There's also the possibility that the pieces of the built-in aren't all attached to each other. We found that out the hard way when we tried to move a bedroom built-in.

If you are able to move it, you'll probably have issues with needing to match the flooring, too.

I assume you live in/near the Twin Cities --- I'm guessing you didn't attend the Bungalow Club's Small Kitchen's house tour a couple of years ago....We went thru 5-6 homes with the original kitchen footprint, but where the homeowners definitely maximized the space.

If you haven't already, you might get a copy of Jane Powell's "Bungalow Kitchens" - great photos and it might get some ideas flowing.

The cabinets were usually ordered from a catalog and arrived as a slide-in unit.

What's on the other side of the wall from the cabinet?