Q: Outlook for Mac 2011 on OS X 10.11 hangs during account sync operation

Have you run the Rebuild option in the Database Utility since starting the new Identity?

If you disable Gmail, does the Identity work correctly? Does Outlook work correctly with just Exchange?

You might like MailTabPro for Gmail $1.99. In Mac App Store (MAS). Nothing to download and easy access to your messages.

https://itunes.apple.com/us/app/mailtab-pro-for-gmail/id430252530?mt=12&ign-mpt= uo%3D4

You mentioned you might try moving to Apple Mail. You could try gmail in Apple Mail and leave Exchange in Outlook. Mail handles Exchange, but overall Outlook is a better Exchange client. However if it won't stay open the few features that are not an option in Mail aren't so important.

Since my last post, the crashes seem to have stopped.  Shortly after I posted, they went from several a day to once or twice and eventually to almost none.  Still have an occasional issue where the Exchange account will lose its connection and I have to restart Outlook in order to get it to reconnect, but that was happening fairly regularly prior to the hand at syncing issues I had before I began posting on this thread and if anything it seems to be less frequent now...  My major gmail account is still working at completing its sync process, but that is most likely because there are so many emails in that account.  I need to archive the older ones from Outlook and delete them from off of gmail anyway. 

Again thanks for your help Diane!  Unfortunately I seem to have lost the ability to select/indicate that a post helped, and I am also unable to indicate that a post "fixed my problem".  Will continue to try, but at the moment I'm not having any luck.  Was able to click that a couple of posts helped previously, but that option is no longer available on any of the subsequent posts, so I'm not sure what happened...