Multiple startup messages over the same connection

Hello,

A question about protocol design - would it be possible to extend the
protocol, so it can handle multiple startup / authentication messages over
a single connection? Are there any serious obstacles? (possible issues with
re-initialization of backends, I guess?)
If that is possible, it could improve one important edge case - where you
have to talk to multiple databases on a single host currently, you need to
open a separate connection to each of them. In some cases (multitenancy for
example), you may have thousands of databases on a host, which leads to
inefficient connection utilization on clients (on the db side too). A lot
of other RDBMSes don't have this limitation.

thank you,
-Vladimir Churyukin