Same Problem. Found the problem (In my case). I had the perpetual "next" button when trying to add an exchange account that I had deleted. 7 hours with Apple support, dozens of different things tried (a few are on this board). This is what worked.
1. Go to user accounts and create a brand new user "test admin" - make it an administrator obviously.
2. Re-start, and log into the test admin account
3. Go to "iCloud" under "system preferences", add your iCloud account under which you have been having problems.
4. Re-start the computer, log back into the test account, go back to iCloud, log out, and log back in
5. Go to "Internet Accounts" under system preferences and attempt to add the problem account. If it won't install, stop reading (you have a different problem than I do)
6. If it works, then you may have the issue that I did.
7. Oddly, the problem was within my "Keychain" - there were conflicting account status within Keychain, and the conflict was sending me through the "next" loop.
8. Log into your original account
9. Finder, Go, "option key" (this shows the "Library" folder), Keychains folder in Library
10. Inside the Keychains folder there are at least two files that conflict with one another. We deleted them all.
11. Restart the computer, log into your original account, Log in and out of your iCloud account, go to Internet Accounts and try to add the problem email or exchange account. In my case, Success!
Good Luck.
