There's rpg systems out there built especially for this type of play. Ars Magica was one that I really loved, but could only convince my friends to play it a couple sessions. (Of course, typical disclaimer on this board, it's not a millionth as good as Shadowrun!) Players switch off as GMs in it and even sometimes share characters. And everyone gets a turn playing a powerful wizard pc.
Anyway, we did some of this at the end of my 2060's campaign. The main reason behind it was to help me out and prevent GM burnout, a constant problem in our group of aging players. (If you can consider the 30's aging) It worked out okay, but right away we found out that despite the best intentions, I'm the really only one that wanted to GM, so it went back to normal. We had tons of GMs when we were young, but nearly all have burned out.
So first, make sure that anyone entering the rotation really wants it and isn't just trying to be nice.
One of the biggest pitfalls I experienced is stepping away from your own player character. I find it impossible to properly roleplay a character without falling in love with the character to a certain degree, and this is magnified if it's one of my favorite characters of all time, which it was in this case. And yes, it's best if you love your player's characters too, but I think quite often most of us love our own player characters best. Just Human nature.
I consider myself an ethical and fair GM, but even so I struggled with this. It wasn't that I was scheming to get my character some mad loot or some stupid drek. No, it's just that it's hard to do nasty things to a character you really love. And then worse, you can over correct and prove how ethical you are by really being hard on your PC, perhaps unfairly so.
It's a bit like the situation where a family member is someone's boss and is unfair to their family member employee, because they don't want to be seen as favoring them. It's not undoable, but it's one of the hardest things I've ever run into as a GM.
As far as plots and story arcs go, we found it worked best with two GMs running two separate arcs, and neither GM knew what was going on with the arc behind the scenes. We used the same group, including the GMs having a PC. Sometimes the GM's PC would be there when the GM was at the helm, sometimes not. The two arcs were fairly easy to keep separate because we each created a different fixer contact and the PCs all got these 2 contacts free. So all stories related to each story arc went through the fixer created by each GM. And not all runs were arc related, but even then each GM used his own fixer and we never touched each other's fixers or johnsons. I asked the other GM to request permission before using my major npcs and agreed to do likewise. it was never an issue though.
I recall it was a gourmet chef/hotel and restaurant owner that was a Johnson the runners worked for a couple times that I didn't want the other GM to touch. The main reason being he was a Corrupted Mage and had a secret kitchen full of Wendigo chefs. None of which the other GM or any of the players knew about or ever found out. And yes, they ate the food. And no, my PC didn't, since he's a salad eating giraffe shaman. See what I mean, favoritism! No, not really, wasn't planned that way.