Please always mail each amended tax return (plus any applicable enclosed payment you may make with it) in a separate envelope. Please do not commingle them, or place more than one amended tax return into a single envelope. To do so only invites confusion and delay with the revenue authorities.
That said, if the amended tax returns are for separate tax years or for separate taxing jurisdictions (for example, federal 1040X returns for 2013 and 2014, or state and federal tax returns both for 2016), then it's generally okay to mail them at the same time -- but still in separate envelopes.
However, if both amended tax returns are for the same year and the same jurisdiction (for instance, let's say that you've amended your 2016 federal tax return twice, as you've received additional documentation), then you should wait to file the second amended tax return until after the first amended tax return is received and processed by the government.
At the very least, you should "stagger" (delay) the mailing of such amended tax returns by a few weeks, as you send in one after the other. That way the government will have the opportunity to process not only your original tax return, if they have not already done so, but process your first amended tax return as well. Thus, when they get around to receiving and processing your second amended tax return, it will "make sense" to the revenue authority, and the numbers will match up with their records.
In other words, a second amended tax return is really an amendment to a first amended tax return. And just like a first amended tax return, the government requests that you initially wait until the processing of your original tax return before filing an amended tax return. So it goes with a second amended tax return.
Hopefully this logic makes some sense.
Thank you for asking this important technical question.