Is there a limit on the number of IRA rollovers that can be done?

Yes, an IRA holder can make only one rollover from an IRA to another (or the same) IRA in any 12-month period, regardless of the number of IRAs you own. The limit will apply by aggregating all of an individual’s IRAs, including SEP and SIMPLE IRAs as well as traditional and Roth IRAs, effectively treating them as one IRA for purposes of the limit.