Don't know about system commander 2000 but,
if it works anyway like the older system commander tool then
it changes the type of the partition table entry of the other operating systems present so they will not interfere with each other.
This should be easily testable by booting the cf card to one of the other operating systems installed. shutting the system down, taking the cf card to your other computer and verifying which data is available.

though the solution to have all four partitions available isn't really easily explained in a workable way aside from saying you need to change the types for all partition entries to correct ones and then change them back to boot from them using system commander 2000.

On a 32GB SanDisk CF:

Basically I create 3 partitions: A 512MB DOS 6.22 (and Windows 3.1 on top of it), then a 2048MB MS-DOS 7.1 (using Phil's Computer Lab Easy DOS Starter pack menu), and finally I create a third separate partition on the remaining CF space for DOS games:

This particular partition is the *one* that I need access to, as if I can see its content on modern PC, I would be able to drag and drop all of my DOS game onto it.

When I connect to my modern PC, the only partition that pops up is the 1st MS-DOS 6.1 partition.

if you don't mind using linux, getting access to those partitions is as easy as one two three.

Yeah windows is like "ThErE cAn OnLy Be OnE pRiMaRy pArTiTiOn!"

what you could try, is go into the disk managment in windows and 'try' to assign a drive letter to the partition you need.

I've only ever had 1 primary partition so not sure how extended partitions behave if more then 1 exist.
I understand why you want/need both your boot partitions been primary, but couldn't your data drive just be an extended drive?
I would assume this would be simple enough for windows to understand and see a primary and extended drive

edit,
Actually does windows support multiple partitions on removable devices? It never used to .
I'm assuming OP is using a card reader in the modern PC so Windows is treating it much like a USB stick or similar where it ignores everything but the first partition.