This idea of accepting some kind of subset is exactly what JVM does. There is a set of rules (IIRC 29 of them) that the JVM bytecode have to follow to be accepted, the one important rule is “stack entries should always be used as a same type”, the rest of the rules are there so that this can be statically checked.
As I said, because of Rice accepting a subset is the only thing which could work. But it only could work, it probably won't because now you've gone from "Impossible" to merely "Incredibly hard" and that's not as a big a change as you'd hope.
