What are my dimmer options in this switch configuration?

I have a setup in my basement where there is a 4-way switch setup, but none of it is run using 3-wire. I’ve seen the term "California 3-way", so that might apply.

There are 3 switches involved:

1. At the head of the stairs there is a 3-way switch. That switch has a two-wire running to its traveler terminals, and the common terminal is feeding the stairs light.

2. In the basement (basically at the bottom of the stairs) there is a 2nd switch, and it is a 4-way. That switch has two 2-wires running to and from it. One goes to switch #3, and the other runs back up to the switch #1.

3. At the opposite end of the basement is the 3rd switch, and it is another 3-way. This switch provides the power and has one of the 2-wires that run to switch #2.

Each of these switches controls a light on the stairs, and the basement lights (there are two).

There is an additional switch about halfway across the basement that controls the far end light alone. I would like to put the dimmer here.

I would like to replace the current basement lights with can lights, and in process introduce a dimmer. I would love to divide the basement in half and do two dimmers, but since there’s just one power loop, I assume this is either not possible or at least would require a ton of re-working the feed.

So I’m starting with step #1…can I introduce the dimmer anywhere on the loop and expect it to work right? Or does it have to occupy a certain place in the power loop?