Question about frostbite on hit and assassin's mark

Hello. In my frost blades-Raider build, I have a three link: Assassin's mark+life on hit+lifetap. On the other hand I m wearing a ring with "curse enemies with frostbite on hit. I didnt think about the mechanics at first but is it that either of them won't be applied to the enemy since I can only have one curse at a time?. I can see in my screen that a curse works on all of the enemies and since mark on hit marks only one enemy I suppose the curse on the ring works and the mark on hit on the link doesnt?
how can i make both two curses work at the same time? Is "you can apply an additional curse: somewhere on the skill tree or should i just look for an item? Or something else that I m just missing?
Thank you

It's on the tree, top right.
You can also get it on hunter influenced chest

hunter influenced body armours can have additional curse mod

non-influenced body armours can also have it from the delve mod

corrupted amulets can have it as an implicit

you can anoint/allocate whispers of doom for an additional curse

you can also use a precursors emblem with additional curse while at max power charges mod (https://www.pathofexile.com/trade/search/Ancestor/G5Jr9WUb)

there are also some unique items like doedres damning for the mod