How do I enter multiple 1099R returns?

Enter them separately, one at a time.

The easiest way to get to the 1099-R entry screen is to simply search for 1099-R (upper- or lower-case, with or without the dash) in your TurboTax program and then click the "Jump to" link in the search results.

Enter a 1099R under

Federal Taxes on the left side

Wages & Income at the top

Then scroll way down to Retirement Plans and Social Security,

Then IRA, 401(k), Pension Plans (1099R) - click Start or Revisit

If you are filing a Joint return be sure to pick which person it is for.

...and to be clear.....just in case your intentions aren't clear...

You enter and file all your 1099-R forms, on one single tax return.   

All your income must be included and filed on the one tax data submission  (your tax return)