Is There an Infinite Number of Generations of Higgs Bosons?

We're pretty sure that there are only three kinds of each of these particles. Is it possible that there's an infinite number of generations? We just can never get to them because they require too much energy? It's a really cool question. What we don't know is why there are three. There could be other kinds of weird quarks that don't talk to the Higgs the same way and do other stuff out there. And there's no limit on how many other weird heavy particles could exist that we just haven't found yet.