What intermediate mail server is suitable in conjunction with GMAIL?

Question

gmail

I have a mail account on a corporate domain. Gmail, purchased an extended g suite business license. The volume today is more than 270 GB.
A lot of people work with this account, Google does not like it and began to block the web interface.
A web server has been deployed on the local network, a RainLoop client has been installed - of course, this is, to put it mildly, not like the Gmail web interface, but at least somehow allows you to work.
The problem is that RainLoop is very slow because it works via IMAP with the Gmail server (how many clients, so many connections)
. The solution seems to be:
1. Collect mail from the Gmail server and put it on the local mail server.
2. Further clients (RainLoop) are connected to the local server and work.
3. Sending mail must work through SMTP Gmail
Questions:
1. What e-mail server will normally cope with such a decision?
2. Maybe someone came across some kind of mail client adapted for Gmail - chains, labels, search?
3. What other crutches can be attached here to get around the Gmail restriction?

Answer 1

https://support.google.com/mail/answer/138350?hl=en

Answer 2

Google doesn't like what? Simultaneous entry from different places? Use vpn.