Can you have multiple closings in a convertible note bridge financing?

Of course. Depending on the situation, additional closings can continue to be held for up to a fixed period of time (such as 30, 60, 90, 120, 180 days or even one year) after the first closing or anytime at the discretion of the board of directors.  If there are additional closings, please keep in mind that (1) interest calculations on each note will be different depending on the closing date, (2) the notes probably should have the same maturity date despite being issued on different dates, and (3) if the conversion discount or warrant coverage is fixed, investors in a later closing might incur less risk than the earlier investors and perhaps the conversion discount or warrant coverage needs to be adjusted to reflect the difference in risk.