Problems with Mail

Mail (Version 13.4) on my brand new iMac (Catalina 10.15.4) is going berserk - I end up with hundreds of repeated mails in 'Recovered Messages' in the 'On my Mac' folder. For example, while drafting an email, a copy is 'recovered' about every15 s. Even after I've sent the message, it turns up in multiple copies in 'recovered messages'. Mails that have been deleted from 'Inbox' or 'Junk' end up 'recovered'. Sometimes mails are 'recovered' but don't arrive in the Inbox (or junk either).

There is a help 'tip' suggesting an account/folder which is having multiple recovered messages is rebuilt. It warns that the folder will be emptied and then 'rebuilt' from messages on the server. However, I've tried this in turn for all the folders ('inbox' 'Sent' 'Junk' etc. for each account), but nothing seems to happen and definitely the problem hasn't got better - quite the reverse.

Any suggestions? What am I missing?

Thanks for any help