I've had 3 going at once, but I don't like doing that.
One of the authors I read has been doing four series at once, alternating. So while he brings out a book every month, it's still four months between books in each series, and that's very annoying for me. Especially since 3 of the current series I've not been reading. I'm losing touch with his releases now as a result and the danger is, when the next book I want comes out, I won't notice it.
I've alternated 2 series, but in the same timeline.
In the 2 series I'm doing now, one is at book 5, with one planned book left to do. The other is releasing book 6 this weekend, and I'll be writing the next 3 back to back before going back to book 6 of the other series. But the only reason that one is not scheduled sooner is because it needs some time to elapse, and what happens now for a bit is boring. So the other series fills in the time.
Regardless, the recommended reading order is the order I write them in.
But having done alternating before, I'm happier doing trilogies in a series instead. Then changing series.