I'm also really interested to see what other people think on this.
Every industry is going to be different and I think this is all about balancing user expectations with your metrics (engagement/conversion)
Whilst getting 7 emails might be overkill for ecommerce/offers that's not going to be the case for everything. If a user were to signup specifically to receive 6x emails on specific subjects and then not receive them that could damage your reputation/engagement as much as sending too many.
Performing some form of contact frequency analysis to understand how the number of emails you send impacts your key metrics (whether thats clicks, action completion, purchases etc is what I would do first and use that to inform your overall strategy. (I do also like DavidO's suggestion of implementing at a user level but having a general strategy is probs a good place to start)
I would also make sure you have a really clear and easy to use method for unsubscribing - so a user can opt-out of topic 1 and 4 but not the others - ensuring they receive relevant content.
