Well, you could have an army of testers but to make that cost-affordable it would have to be outsourced. You could also spend time prioritizing tests based on risk to fine-tune how much you test each iteration. Another option is to ensure that your Dev team is creating a good suite of unit tests that are run each build.
Also, having your Dev team help on regression testing can reduce your time to release as well as foster a team mentality of getting it done-done. It might also motivate them to write their own automation!