I had one. Had access to their transcripts and they did have one already on file. 

Prior preparer auto-filed extensions for them. A bad deal, particularly when you wanted to set up a payment to be paid automatically with the extension.

Prior preparer did not file anything.  I was the prior preparer for one of them.  It's too much of a coincidence for (now) FOUR in a row to have been rejected!!!

Can you still do an IRS DirectPay Extension Payment if there was already a 4868 filed?  I think so but I stay out of the tax payment processing business so I'm not sure.

Yep you can, can always process a $1 payment in case you were worried enough. 

I am going to go ahead and file paper EXTs, with a copy of the rejections.