Yes! The key to sitter success is being proactive and flexible, so you can apply for as many sits as you want to and then make more firm arrangements as things progress.
Just remember, once you've agreed and are confirmed for a sit, this is a firm agreement and you won't be able to apply for sits on the same dates. We know that many sitters confirm back-to-back sits, so you are able to apply/confirm sits that end and start on the same day.