By-Feature Interaction Control
In addition to the more standard interaction control features (unfollow, block, mute, content tags) which can act as they do on other services, the option to selectively modify interactions with accounts on a case-by-case or Group basis would be very useful. Some potential options:
They Can/Can't see my posts on their feed. They Can/Can't DM me. They Can/Can't see posts I tag with sometag. They Can/Can't see my account at all (as a normal block). They Can/Can't share with my posts. They Can/Can't Reply to my posts. They Can/Can't like/fav my posts. They Can/Can't Follow me. They Can/Can't Alert me to posts (via mentioning/pinging). I Can/Can't See their interactions with my posts. I Can/Can't See their posts on my feed. I Can/Can't see their DMs to me. I Can/Can't See their posts tagged with sometag.
Essentially, giving a very fine level of control to the user over who can do what to/involving them, and allow partial muting and partial blocks.
Note that I think this should be an option in addition to the faster, more intuitive and easier-to-use Block and Mute buttons (which could just act as a shortcut for a set of these options applied to that account when you hit the appropriate button)