Thanks, Wes, and thank you Jason for asking a favorite question! First off, there isn’t really a consistent answer to this. Which is why I guess we’re a great bunch of people to do business with! 
My background is 14-member multi-type, based largely on the fact that it involves university, community college, K-12 school district and 4 public libraries spread out over 90 miles and four distinct counties. In a multi-type such as this, what we have in common is the software; what we don’t have in common are the patrons, policies, or processes. Thus, we do not share patron records (faculty use end of semester dates, but get 2-3 week checkouts at the public library. Kiddoes at usd250 may get 2 weeks, but get 2-4 weeks at the public library for checkouts. Faculty at usd250 may get a year checkout at the school district, 2-3 weeks at the public library, and maybe a semester long-checkout at the university. So. We all maintain our own patrons, and all have separate cards and privileges. Unless that particular library is a “branch” and is used to having things decided for them as a main library with “two branches” - it may be best to share servers but not records.
Another question to ask, are you all on the same fiscal year pattern? In our case, campus runs July-June, publics run Jan-Dec, schools run Oct-September. So we don’t clear statistics based on “end of year” because my end of year is not necessarily your end of year.
Bibs. Yes, we share bibs. We encode using the 049 tag to indicate “who has planted their flag” and claimed a piece of the bib. With Sierra, you can assign “locations” and even “libraries” (branches) but if you are a consortia you also will have “scopes” - while scopes I think were generally created for public to “scope their view of the online catalog”, scopes also use staff permissions, so, as a cataloger, I would have permission to edit the bib, but if I am at library A, I do not have permission to edit, delete or create an item at “library B” - Scoping has an inanely complex setup to it, but if set up correctly, it does protect the ability of library A to not muck with library B’s items, patrons, orders, etc. In other words, separate, and different.
If your three libraries are all publics, and you all agree on lots of things, you might be able to work, theoretically as “branches” with policies that work for everyone, but in mixed-type situations the tag line really is that everyone agrees… " to do it differently" -
I won’t go too much further into this, but this may give you a bit of something to think about. If you have any other questions offlist, my email is sjohnssmith@pittstate.edu - Thanks, Susan