What you describe is a direct rollover. There are no tax consequences, and there may not even be a 1099-R issued. Even if a 1099 is issued, the transaction is not taxable. You can do as many direct rollovers as you like.
If you requested funds to be withdrawn from an IRA, either electronically or by check, which you then forward to a separate IRA, that is an indirect rollover. You can only do one indirect rollover per year, and you must complete the rollover within 60 days, or else the distribution will be taxable.
