Abstract high-level framwork for #SAT
DPLL can be modified to count model, i.e. to solve #SAT. So yes, you can modify the Abstract DPLL for #SAT.

However, AFAIK DPLL is not state-of-the-art for #SAT, so a DPLL-based framework is neither important nor useful. The Abstract DPLL is useful because it covers most state-of-the-art DPLL-based SAT solvers.

You can take a look at these following papers:

1) Counting Model using Connected Components. It is implemented in the tool RelSAT.

2) On Compiling CNF into Decision-DNNF. CNF is compited into DNF to count model. The authors have a tool, c2d, implementing this approach.