There were a couple of events well over a year ago or so when I flew 3 accounts at the same time.
I ran 2 accounts on my PC (ALT TAB) and the third on my wife's (sits right next to mine on the same workstation).
My wife's PC had an identical setup, so all controls and key sets were the same.
One account was my Sons the other my Daughters and I did it to help them out with some cash.
It was one of those lugging CG's and as long as I staggered the timings, it was reasonably easy.
All was manageable until one, two or all three ships got interdicted, then the workload went beyond any normal human capabilities to pilot them
Not long after that, there was a season update which prevented the game running on the same PC more than once.
I know there are ways around this, but my daughter lost interest very quickly and my Son gained enough cash to not need my help any more, so I haven't bothered doing.
I now have three accounts, I bought a second for myself because I like doing restarts without deleting my first CMDR and I now have my Daughters as a third.
Only my first account has access to beta and only my first has Horizons.
My Son still plays on his account and has Horizons, but no beta.
So I can't help with an up to date test.
I can imagine if Horizons came on sale, I'd be tempted to upgrade my second account for an extra pip.
From what I could figure from the Live stream, you only get one extra pip for a fully crewed ship, not one extra pip per extra CMDR, but not 100% sure.