That depends on what you mean by “the same time”. You can, of course, study for both tests within the same study session if you’re good at staying organized. But they’re still two very different tests, and being prepared for one doesn’t necessarily mean you’re prepared for the other.
For example, if you’ve focused on SAT prep, you probably haven’t brushed up on your fundamentals of science, which means you’re not ready for the ACT’s Science portion. You also wouldn’t have practiced writing essays, which would leave you unprepared if you opted to take the Essay section on the ACT. And if you’ve been focusing on the ACT instead, the no-calculator Math section on the SAT might trip you up.
It’s better to do one thing well than to do two things poorly. By all means, take practice tests for both the SAT and ACT and see how you do, but once you’ve figured out where your strengths lie, focus your energy there. Play to those strengths and devote most of your study time to the test you most want to send to colleges, even if you do decide to take both. Pace yourself and be sure to schedule your test dates wisely. Don’t stretch yourself too thin and end up with just “okay” scores on both tests, because you want to stand out, not blend in.