You'll probably end up taking twice as long to get your license? I believe there is some allowance for training on multiple types during a PPL, but it's really intended to allow a few hours (say 1 or 2) on something else; I seem to remember that there is a requirement for a minimum number of hours in whatever you do your test in. The only type you'll get on your sparkly new license will be whatever you do your test in; you'll still need to do an approved course to get any other types added.
Training on multiple types seems like a good way to make your PPL cost a whole lot more, in my opinion.
-- One of the non-chaps