We have 29 databases.  The one that kicks me out is 31MB.

I have no trouble logging into 13 databases.  Two give me -6123,-0 errors, and 13 give me -6000,-832 errors.

There are two additional databases that generate -6000,-832 if I go through the "Open or Restore Company" option but open fine if I select them from the "No Company Open" screen (they're in the list of recently used databases), which is even more bizarre.

As much as I hate calling Support, I'll be doing so as soon as I have a block of time when it's safe to work on these things (i.e., I won't be interfering with other people's work).