Technically, yes. In some cases, transferring your balance two or three times might even be what's necessary to finally pay off your debt. But unless you have a firm understanding of how you got into debt in the first place and a plan for getting out of debt, you won't be working toward a solution.
While transferring your remaining debt to a second balance transfer card may allow you to pay off your balance without monthly interest or a fee, it's important to note that there are too many variables for multiple balance transfers to be a failure-proof debt strategy.
For example, your card application could be denied, your credit limit could be much lower than you anticipated or your transfer request could be denied. Credit card offers could also change, making it difficult to plan ahead. For this reason I recommend selecting a card that allows you to pay off the full balance after one cycle if possible.