Using the same data as last time, six months of a weekly dance plus a year of dance weekend bookings, I looked up the instrumentations for each band. Here's the data as an ugly table:

You can tell there's a lot of overlap between entries, though, and a table doesn't represent this well. It's easy to see that all the bands have fiddles, but is it more common to have a piano or a guitar? Or both? I played around with ways of visualizing this, and while I'm not completely satisfied with it, I do have something:

 Fiddle 172
   Guitar 117                    Perpetual e-Motion, Uncle Farmer
     Flute 39                    The Mean Lids, Crowfoot, Maivish
       Bass 6                    Wild Asparagus
     Piano 24                    Great Bear Trio
       Drums 6                   Relative Harmony
         Cello 4                 Gallimaufry
       Whistle 2                 Wild Hair
     Bass 13                     The Stringrays, The Gaslight Tinkers
       Mandolin 4                The Contrarians, On the Fly
       Banjo 2                   Euphor
       Accordion 1               T-Acadie
     Clarinet 9                  The Figments
       Trumpet, Trombone 8       Elixir
     Drums 5                     Contraforce
       Mandolin 3                Notorius (quartet)
     Fiddle 3                    The Dead Sea Squirrels, The Cosmic Otters
       Mandolin 1                Atlantic Crossing
     Banjo 3                     Sassafras Stomp
     Accordion 3                 Anadama
   Piano 55
     Bass 24
       Drums 8                   Arigana Highway
         Banjo 5                 Hotpoint String Band
         Flute, Accordion        The Clayfoot Strutters
       Clarinet 6                The Latter Day Lizards
       Accordion 5               Tidal Wave
       Fiddle 4
       Flute 1                   Spare Parts
     Mandolin 22                 Nor'easter, The Free Raisins
       Drums 7                   Lift Ticket, The Syncopaths
     Drums 6                     Party of Three, The Coffee Zombies
       Trombones, Accordion 3    Giant Robot Dance
     Hammered Dulcimer,
       Flute, Accordion 2        Swallowtail
     Fiddle 1

This shows that once you've got a fiddle 117 of 172 times you find a guitar and the remaining 55 times you find a piano. Then if you got a guitar, the most common additional instrument is flute, followed by piano, and the bass. I've put in examples of bands in each category, but there are of course many others.

(One thing I don't like about this categorization is that it's not very stable. Imagine about a third of bands have guitar and piano, a third have just piano, and a third have just guitar. If guitar is slightly more common than piano this chart will put all the guitar+piano bands under guitar, exagerating its frequency, while if the piano is slightly more common we get the reverse.)

Another way of looking at this is as an approximation for "given instruments A and B, what are the candidates for C, and how popular are they?" Or possibly "given A and B, how much do each of the candidates for C add?"

Update 2014-04-02: At Mac's suggestion I've added a chart:

[1] For example, while the Free Raisins play some as Fiddle/Trumpet/Piano or Fiddle/Accordion/Mandolin, we're primarily Fiddle/Mandolin/Piano.