This is absolutely possible. I wired LEDs under my home bar and across the back bar and can have different colors in any section, or the same colors all around through the use of a remote control. The only limitation I had is the remote control is an IR remote control as opposed to an RF remote control, so the receptor point needs to have a line of sight access to the remote. I do believe that they make an adapter that would allow you to use an RF remote control.
Each LED strip runs on a 12 V DC power supply and you can cut each LED strip to the desired length and then position it where you need it either over or under your cabinet. They make small extensions so that you can run different strips on the same powered circuit to achieve the look that you want.
I have purchased these from an eBay store.
5M RGB 5050 SMD Non-waterproof 300 LED Light Strip Flexible + 44 Keys Remote | eBay
There are many more sellers that offer similar items. These strips can be cut and linked to small adapters (plugged in) that allow you to negotiate corners or small gaps, as well as extenders that would (in your case) allow you to skip over one cabinet and go to the next and run an additional strip.
You would need a few power supplies for your particular arrangement, but this is definitely do-able and wouldn’t be very costly. Good luck.