No you cannot share editing. This is mostly a AGOL limitation as you must be the owner. This info is backed into the .info file so I am not sure it can ever change.
Also no on a network location. I do not have a reason for that one, 123 thinks its a risk I guess.
Both of these have been asked for dozens of times over the years so this is a dup.
Slim options but a bat file that copies the files to the network as a backup is about it. You could also try having a master account that all the editors share if your IT will let you. You would still have to do the dance of copying files to the network, then have the other person copy down. I think this would turn out to be more hassle then it is worth.
We did do a big migration once where we moved all the content from an old user name to a new one. We were able to move to a new owner in AGOL then edit all the info files and it worked. But this was a one time deal and not something that would be a regular thing.
You can also move owners then use the download option on connect but I have seen issues here with media files but maybe that is fixed now. But still that has to be one owner problem.
Our big fear is if the form owner quits or gets sick we are totally stuck. As an enterprise we cannot have this really but unfortunately much of the Esri software stack is not very enterprise ready.
Sorry wish I had a better answer for you.
