Some testing I did with Tecsee Medium switches.
These will work 
DSA - No collisions
DCS - No collisions
SA - No collisions. Tested both SP and Maxkey
ASFA - No collisions. Stems too loose for this profile. You’ll have to add teflon tape to every keycap.
HSA - No collisions
These won’t work 
GMK - Collision on all rows
KAM - Collision
KAT - Collision on all rows
MT3 - Collision on both ABS and PBT
GSA - Collisions on all rows
You can certainly use any keycaps on these switches. But the ones listed as “will not work” collide with the upper housing of the switch (usually on all sides and not just 1). The result will be a noticeably weak sounding bottoming out.
I was pretty excited to find out that HSA profile keycaps work. I love this profile, and putting it on linear medium switches is a refreshingly unique typing experience.
Feel free to share your findings if you test out more profiles. In general, if the keycaps are thick or have any support structures for the stem, they will probably collide with the tops of Tecsee Mediums.