iTunes - 2 disc opera, only one disc will file under Compilations

To ensure that a compilation album is correctly identified, two tags need to be correct. So your specific issue indicates that disc 2 is not correctly tagged (not an uncommon problem).

Try this:

• select all the songs (tracks) on disc 2
• click on Edit/Get Info (and when the question box appears, tap on Edit Items)
• using the picture below as your guide:

• note the difference between the artist tag and the album artist tag. We are interested in the album artist tag. Do not change the wrong tag in the following step
• make sure that the tag album artist contains the text Various Artists (type it in if it doesn't). If the box contains the text "Mixed" in greyed out italics, that indicates that some tracks have different text to other tracks (i.e the information is inconsistent)
• make sure that the compilation tag has a tick (checkmark) in the box (as shown in the screenshot). If there is a dash in the box (as shown below), that indicates inconsistent information:

I would that add that disc 2 should be set as Disc 2 of 2, disc 1 as Disc 1 of 2 and then both discs should be given the exact same album title (and a common Sort Album title if this isn't blank).

tt2

In the Songs view of the library make sure that both View > Column Browser > Group Compilations and View Column Browser > Use Album Artists are ticked.

tt2

I wonder if the issue with the Oberto is that all of the Artist values are the same, so it doesn't fit the standard iTunes/Music criteria for a compilation which is an album that is a collection of tracks by different artists.

FWIW with classical music I generally relegate any performer/conductor details to the comments field and use the full name of the composer in Artist, Album Artist, and Composer fields, and fill the corresponding sort fields with <Surname>, <Initials/Forenames>. That way, for example, everything by Giuseppe Verdi is shown under that artist name, sorted as Verdi, Giuseppe.

tt2