After using the multi-account feature in the Desktop Client for a while now, I have some suggestions on how to handle this UX-wise.
A problem for me is that I have to switch accounts frequently, because the other accounts are not crawling for messages in the background. The effect is that I rarely switch accounts at all. If there was a sidebar showing a logo per account with a small notification number or so how many messages there are, that would help a lot already.
To save energy & network usage on Android, this could be combined with this feature proposal where someone proposed a disable button for accounts.
Wire does it quite well, they could be an inspiration here.