Which CRM is most tightly integrated with mail?

Question

CRM

The task is this. There is a web studio, there is a mailbox where mail arrives, which in one way or another relates to the work of the web studio. Letters are also collected there from the mail addresses of clients, to which reports on the operation of their sites, for example, or other technical information are received, letters are collected there that relate directly to the web studio itself, in general, a kind of letter aggregator. Correspondence with clients and new applications from clients also fall there.
And there are various CRM systems that allow, in addition to their basic functions, to work with mail as a source. The task is to collect letters from the mentioned address in full, and not only those that are directly related to customers or some other contacts that are in the database.
At the moment, Bitrix24 was found as the closest option to this, since it can integrate with such a mailbox (CRM / Settings / Integration with mail), but the trouble is that it can only get letters from there to itself with contacts existing in the database, or, as an option, create new leads from letters if the senders' mailboxes are not linked to any of the contacts in the contact/company database in the system.
That is, for example, a report comes there from a certain service used by the web studio, and this letter can be seen in Bitrix24 in only two versions - either the mailbox from which it came is specified as a contact/company email, or a new lead will be created from this letter , although in fact this lead is absolutely not needed, since it is just a letter that I would like to see in the system, without going to the mail service interface and processing it there, but to see it simply as a letter, not attached to anyone and not processed as another lead or something like that.
Naturally, a nice bonus is that this system is free with this functionality.

Answer 1

eWay

Answer 2

We have crm and erp. But we failed not only to integrate both systems, but even to figure out how to do it without increasing the fragility of the entire system. As a result, we took the p2 wordpress theme as a basis; the logic of correspondence on tasks ala ticket system has already been implemented, and there is a mail pickup plugin, which we are now trying to fix so that it can work on shared hosting.
We take free software where possible because we don't like the idea that we can't customize the system for ourselves. P2 in this part is the ideal solution for us, free and free, which is simply finished with its own plugins or others, of which there are also enough.