I've been messing around, but haven't learned any actual tunes. I like to play the "1" beat with a lower string at the same time. Sometimes I double-up on "3" too. Lessee if I can do an example of each. (You know, it ain't easy to type with a thumbpick on!)
Am G
|----------0--|------------
|--0-1--------|--0------0--
|--|----2-----|-----0------
|--|----------|---------0--
|--0----------|--2---------
|-------------|------------
So what is the picking pattern you're tired of? I'm new at this stuff, and I may not know THAT one!