Designing Kitchens and Bathrooms - Leveling Kitchen/DR floors question

OK, I have a 1906 house that has a difference in the level of the floors in the kitchen. I guess the kitchen used to be much smaller, and the back part of the house was mostly a porch. At some time the back porch was enclosed, rooms were added/created, and the kitchen was expanded (possibly an entire addition - no records that I could find). Anyway, the back third of the house has probably 1 layer of subfloor, but the rest of the front of the house has 2. I've looked into the heating vents and was able to see 2 layers of 3/4" fir, plus 1/4" plywood for the linoleum -- this is in the front 2/3 of the house. The back portion I can't really be sure (I've looked at a hole in the back porch floor from an old plumbing vent), but it seems there may be only one layer of subfloor. There is a "slope" in the floor (linoleum) When the cabinets were replaced about 10 years ago (we didn't live here), they had to scribe the bottom of one of the cabinets to fit the slope of the floor. So, next month I am planning on taking the floor down to the same level, then putting on hardwood. My question is: Can I do that without having to remove all the base cabinets first? I was planning on removing most of them, but there is a large corner cabinet (with the scribed portion) that may be especially challenging. I want to keep the cabinets intact - I don't want to destroy the countertops. We will replace those next year after we get our tax refund. Thanks for any help.

You can install new flooring around the cabinets, but if/when those cabinets are replaced and if the floor plan is changed, you will have to piece in the floor to cover empty spots.

As for sloping floors, old houses sag, and old additions are sometimes not properly supported, making them sag more. Fixing those floors opens a large can of worms, which can get really expensive.

I pulled off the trim around the cabinet and found they only shimmed up the low side of the cabinet to make it level. Now, to clarify -- the 'slope' in the floor is the linoleum sloping down from one level of flooring to another. It's not as complicated as you make it sound. It's just a lot of work to bring the floor down to the same level. I will probably have to remove all the base cabinets to cut out the extra layers of flooring. Also, any tips on removing the cabinets without destroying them (especially the countertops)?

Assuming a laminate c-top, likely screwed at the corner of each or some of the cabinets from underneath. Remove drawers and stick your head under, you should see screws thru the angular blocking wood at the cabinet corners. Sometimes, a dab of silicone caulk was used, but it should come loose with gentle persuasion with a wonder bar. Then carefully lift off the top. Cabinets are usually screwed to each other behind door hinges, but thru the frame, and to the wall studs behind. If they don't lift out fairly easily, look for screws thru the back cabinet wall or into the floor.

Actually the counters are tile with an oak trim, but I'm sure it was probably attached the same way. However, the problem cabinet is a large corner unit, so I'm afraid the tile will crack when I lift it up. Any suggestions? I know I can separate the individual cabinets -- I'm just worried about the counters.

I would doubt that you can lift a tile top off without some damage, at least to the grout, if not cracked tiles. And bring lots of help, it will be heavy. It is likely on 3/4 plywood underlayment with duroc or hardibacker over that, under the tile.

I'm thinking that maybe I don't have to remove the cabinets (except the ones I am moving anyway). The differential seems to be 3/4" or less - I took off the trim and looked. Once the new floor goes in, any gap should be covered by moulding/trim. The old 1/4" underlayment only goes right up to the cabinet base, so the flooring was laid after the cabinets were installed. The only cabinet I have to move in order to make the floor underneath lower is a small single drawer/door combo unit. It should be easy to move without removing the countertop. I'm not sure about the island - it's 4' X 2', so it might be pretty heavy (even after I empty it out). Any thoughts?