I can't reliably answer your question, since I never used exchange and was never invited by people using exchange.
Just not the people I hang with hehe.
But I can give some thoughts and experiences of my own.
In SOGo you can add multiple IMAP-Accounts but since you are speaking about aliases, adding them is not even necessary, since they are just aliases and get delivered into the same Inbox. So I am not 100 % sure if you are really talking about aliases and not secondary accounts used as aliases.
To the topic of calendar invitations like Exchange. No idea how Exchange handles this, but even Thunderbird can create calendar events with participants and will send invites as mail.
SOGo will do the same. Maybe you should just test it in SOGo and then circle back here to explain what is missing or needed for "the Exchange experience".
There is also:
rallly doodle poll alternative
cal.com event-juggling scheduler for everyone. Focus on meeting, not making meetings *1
Easy!Appointments appointment scheduler
*1 Note about cal.com, this is more for people booking a meeting with you based on your time available based on configured business hours, already blocked times by other events in your calendar and more.
This can be abused to be something else tho
I used to use cal.com with some friends because you can add multiple caldav calenders into 1 account for checking for conflicts when scheduling.
Meaning we, 6 people, had our 6 private calendars setup in one account, so we could use cal.com to see exactly when each of us had time.
Used this to schedule a DnD like event, but people got sloppy managing their own private calendar, so open slots were not always accurate.
WELL I hope this helped somewhat and was not just some random rambling
