This isn’t really about alternate chords so much as alternate fingerings. This is probably pretty basic stuff, but since I didn’t manage to figure it out on my own, I’ll share it.
Fretting two strings with one fingertip was one of the first technique lessons I got from my current mentor. He encouraged it both because of the economy of motion and because picking up two strings with one fingertip frees up a finger for chord embellishments.
I use this C chord most of the time now:
With the 3rd taken out of the high E string, it’s almost a power chord, and hitting all 6 strings gives a big booming C that works well for progressive bluegrass. Alternate picking the bass notes is easy from this position, too.
This Am chord I had seen Doc Watson use, but I always figured my fingers were too small until I tried it:
This F chord I still struggle to form cleanly, but I’m trying:
The idea of fretting two strings with one fingertip seemed beyond my capabilities until I tried it, but it’s actually not too difficult. The middle of the fingertip rests right between the strings and the edges of the finger pad apply enough pressure to sound the notes. Like everything else with guitar, it just takes repetition.