I'm wondering, are there any papers or research dealing with visibly pushdown automata, but allowing words, rather than single letters, to be pushed onto the stack.
Alternately, a construction which allowed for symbols to be pushed on $\epsilon$-transitions could achieve the same goal.
Obviously, such variations can be formed, but I'm wondering if it ruins the closure and decidability properties that make VPAs interesting.
I'm looking at a construction where use the stack as a counter, incrementing it by constants based on the initial symbols read, then counting down based on other symbols read.
For anyone who doesn't know, visibly pushdown automata are ones where the alphabet can be divided into pushing symbols, popping symbols, and symbols not affecting the stack at all. The choice of pushing versus popping is entirely determined by the current symbol being read. They're closed under intersection, union, concatenation, star and complement, giving them a wealth of decidable properties. See this paper for more.