Another keeper from Terry Stibal on the topic of cutting parts from theater show music:

I would disagree with choosing the baritone as being the saxophone to eliminate. Instead, I would opt for the tenor. The reasoning goes something like this:

Baritone saxophone in shows is used three ways: as a saxophone choir member, as an additional trombone, and as the best blending of the bass instruments to "balance" out against everything else.

Tenor saxophone in shows is a bit more problematic. With the exception of the period piece musical that tries to channel the 1940’s, it is not normally going to be a significant solo voice. Exceptions here might include Evita, where there is a huge tenor solo in the one true female ballad, but for the most part the tenor is just filling in an interior harmony part. And, that’s pretty well it.

While the tenor (and the much more lyric style alto) will get used to "fill out" string parts at times, neither of them approaches the baritone in terms of overall utility.
Just this week I have been rehearsing a production of The Music Man, and it is almost scary to see just how much of that "Seventy Six Trombones" effect is coming out of the mouth of my baritone. While the bass trombone player is providing a portion of that "bottom", he’s nowhere as agile or "plastic" as I can be on the baritone saxophone. Listening to the three trombones try to make up the seventy six trombone volume and spread by themselves is kind of fun by itself.

Two horns that I would keep as the last-ditch, not to be cut instruments (after the solo clarinet, flute and alto sax voices, would be bass clarinet (very vital, even more than the baritone, due to female vocal accompaniment) and baritone sax, in that order.
One other thing: if you can play (and have) a baritone and bass clarinet (in addition to the normal flute and clarinet), you are much more employable. Every year, I’m first pick for several musicals while my alto and tenor only buddies have to compete for their limited slots.

Something to consider.

In all my years of doing shows (over thirty different shows, with many repeats within those thirty over the years), only once did I need to come up with tenor sax/clarinet skills to get through the doors. (Threepenny Opera; four or five different productions of same during the period). All of the rest of the time it has been mostly clarinet/bass clarinet/baritone, with occasional excursions to tenor sax, alto (to fill in a missing book), soprano (one time) or bassoon (more times that I care to think of, including two shows this spring).

When money starts becoming an issue, most musical directors look to cut the Reed III and IV books (in an five book show). Very often, that means the tenor saxophone/clarinet/oboe/Engish horn player sits that one out.

On the other hand, if you can handle both the oboe and English horn parts and can "get by on tenor and clarinet, you have increased your "desirability" ten-fold. In that, they will be more interested in your oboe/English horn skills than they will your saxophone skills.

One other thing: I’ve never seen a show that calls for alto clarinet. It’s probably not a good idea to invest in one for pit work. Contra-alto, on the other hand, I have played in a couple of productions of On The Twentieth Century, and The Producers also foists this off on the baritone/bassoon/bass clarinet player.

Terry Stibal,  leader of Houston’s Sounds Of The South Dance Orchestra
info@sotsdo.com