ok. here is what I did.
I opened foobar. Selected 5 albums with works with multiple composers (artist=composer in my tagging system)
Copied all those files to a temporary directory.
Opened them in mp3tag. Set the compilation to 1 based on the sub-parameters on my previous screenshot. I didn't notice any tag field chaanges? and when I try to open these in foobar for android, they are grouped just as I wish (based on album names)
Other fields look fine to me?
But now I am paranoid 
Just to be sure and just as a side note:
You suggest to set the ALBUMARTIST to "Faith Hill" (as she is set to ARTIST) for her ALBUM "Faith", right?
(Even if the Track #9 "Just to Hear You Say That You Love Me" is a Duet with Tim McGraw).
And the ALBUMARTIST to "George Michael" (as he is set for ARTIST) for his ALBUM "Faith", right?
And only for albums like "The 50 Greatest Rock Songs" where 50 completely different artists build a compilation, you set the ALBUMARTIST to "Various Artists", right?
I am always very reluctant to accept what a player displays.
Could you post a screenshot of the extended tags dialogue of a modified file?
That screenshot should show that there is a field called COMPILATION and a field ALBUM that is not equal to "1" (unless it is the Beatles album)
Correct - and the Artist field on this duet track can be "Faith Hill; Tim McGraw" or similar depending on how you wish to potentially separate the multiple Artists in this case. (This is a totally different topic though)
Correct (I don't recall any additional featured performers on this album)
Correct - and the Artist field can all list the individual Artist(s) for each file.
It is worth noting that in many cases the Albumartist and Artist fields may be identical. There is nothing wrong with keeping the duplicate data as this doesn't use up a significant amount of data. But it certainly helps to keep a large library in check when it comes to browsing!
Here are the 5 albums thrown into a test directory vs the very same albums without my changes to the original tags... and screenshots from foobar android.
thank you all
https://we.tl/t-xPcopSsREd
I cannot reproduce it.
This what happens in my MP3tag:
Column definition
Top file has set "Compilation" and that is displayed.
1 file lower has nothing in COMPILATION, therefore the column ALBUM is empty.
Please see the tag panel and the Contents of ALBUM for both files:
Now I set the "1" into the column ALBUM:
The "1" is saved to %ALBUM% - which also appears in the tag panel. The original data in album gets replaced with the 1 just set in the file list.
So, what did you really do?
so far nothing. And I'm glad, i didn't do anything?
Well...first of all I appreciate your help.
I notice that in the left column you have "album" highlighted and compilation is not listed.
This is knowledge from many years ago: If you set compilation to 1, different artists are recognized as various artist under the same album?
As MotleyG also mentioned this is an itunes feature. foobar android seems to be happy with it?
Let me further confuse you, though:
I was replicate the same positive result without messing with field/sort by boxes.
Set to 1 and done. no changes to additional fields such as albumartist etc?
But I am not touching anything for now.
thanks again to you all for your time and help
The label of the column does not matter.
I just set my column labelled "Album" to the definition that you used:
Value:%compilation%
Field: %album%
(which causes the effect I documented).
It would be nice if you could stay with MP3tag dialogues and functions and corresponding screenshots. The foobar screenshots do not help as such as players often have a mind of their own.
Still, I even took the effort and loaded the original and the test folder onto my mobile and started foobar.
Apparently, foobar interprets the COMPILATION field and sets "Various Artists" as ALBUMARTIST automatically as soon as the COMPILATION field is filled.
This still does not make your workflow and column definitions in MP3tag more plausible.
Or the other way round: as soon as I use the same column definition and set COMPILATION to "1" in the file list (it would make much more sense to use the tag panel for that purpose), the data in ALBUM gets replaced with "1".
Let me start with an update:
here are the latest screenshots. Compilation set to 1.(field and sort by boxes are empty)
Foobar android does a good job sorting the albums based on album names DEPENDING ON HOW BIG THE LIBRARY is.
When you go beyond a certain amount of tracks, (don't know what the limit is) unfortunately foobar fails to sort them out.
At this point this is a player issue, not mp3tag issue...
I guess for large libraries your previous suggestions (adding albumartist etc) will be necessary.
There is a reference to issues due to large libraries at this site. Scroll down to "verdict" section at the bottom of page:
Do you set COMPILATION in the tag panel?
I see an element there that is called "Compilation".
The current column definition (from the screenshot) only displays the contents of COMPILATION if there is any but does not write it to any field.
40K+ tracks is too much I guess...
I'll move to a foobar forum and see if they have a workaround.
Would be happy to update this thread if I find out a solution.
Thanks again
What do these red 2 cirlces mean?
i am setting compilation to value 1
Where? In the tag panel? In the extended tags dialogue? In the file list?
I'm sorry I don't know how to be any more clearer?
Please also see my previous post Script to update "compilation" tag? - #30 by rond056 additional screenshots.
COMPILATION (1=on 0=off) groups albums with multiple artists under same cover in the album that they appear.
I guess this really depends on how big is big? 
I would suggest your 40k is bigger than many but certainly nowhere as big as I have seen others post about online. I have a library of just under 26K myself, and Foobar Mobile on both Android (my DAP) and iOS (iPhone12) handles it just fine.
Most of these types of issues are more about the player, and what they can, or more often, cannot do.
The metadata you include for your library will be the biggest influence here. With more details and a full compliment of complete tag fields, most apps and programs will be well-behaved (I have stumbled across that site myself, some good insights there!). There are many tools in mp3tag that can help to get these filled in from folder and file name structure, and additional web resources can be used as well. But with limited metadata info, GIGO.
Hi I'm back
I noticed an album that seemed to be behaving as planned.
I checked the metada on foobar. Wierdly it had an itunescompilation value set to 1:
I immediately opened the files in mp3tag.
NO SUCH TAG
What to do please?
The problem is once again a tagging issue. I think I was able to demonstrate that size of the library affected the way "compilation" tag behaved under foobar android. But how about "itunescompilation"? why isn't that not listed under mp3tag??
Thank you!
Please note that every player has its own naming conventions.
So, that what foobar shows as itunescompilation could well be shown as compilation in MP3tag.
Thanks for your reply. Please note that I removed the compilation tag completely from the metadata in mp3tag.
It no longer exists. The extended tags no longer include it.
Apparently itunescompilation is now a metadata that is no longer recognized by mp3tag. Seems ok with foobar.