How do I go from a 3-way switch controlling my basement lights to multiple 3-way switches?
What you're really looking for is zone control.

You still want the ability to turn all the basement lights on/off from the 3-way switches.  In fact, the ability to do so is a Code requirement, since the stairwell lights must be on a 3-way.  However, you want the ability to extinguish lights in areas you don't need.  

So what you can do is add an additional block of switches on the "switched side" of the 3-way circuit.  That is, the side after the 3-way travelers.   In other words, don't overthink it.    

The simplest way to do this, by the way, is to install lamps with pull chains.  But we can do it with real switches.  

Let's start with a simple view of what a 3-way circuit is.  (And by the way, I strongly recommend you get colored tape and actually mark your wires these colors - because things will get really complicated if you do not!!)



Don't overthink it: don't mess with the yellows here. As things are, the "red" is on or off according to 3-way command. It branches out to your multiple, various lights including the stairwell light.    So we're going to have the "red" serve as the power input to another bank of normal (1-way) switches. They will input red "switched-hot" and output "switched, switched hot" to those lights you want separate control of.  

Now, you can control the bunch with the 3-ways, and select which of the bunch turn on at the supplemental switches.  

The stairwell light proper, since by law it must be under direct control of the 3-ways, will still get its power off the red, and will not be under a subsidiary switch.  

Is this conservation necessary?

The better thing to do might actually be say sayonara to incandescent lights, and convert to LED.  Then you won't need to worry about the electric bill.