In vanilla, there is a bug where if you set multiple objectmods to have the same loose mod in the creation kit, the game still requires you to build a new copy. This proof of concept mod gets around this and allows sharing of a single loose mod between multiple weapons, without the use of an intermediate attachment point and still allows different effects to be applied to each weapon; the separate objectmod records are retained.

The way I did this was by giving the loose mod its own new scrap component, and adding a new recipe that uses that component instead of the base components. Which recipe is shown depends on if you have a copy of the loose mod or not; the base recipe shows when you have none, the new recipe shows when you have at least one. It can be in any caravan-linked workshop, which is what the script checks for.

There is only one small but fairly annoying bug. If you have only one of a universal mod available and you take it off of a gun, you cannot reapply it (to anything) until you either exit and re-enter the workbench or build another mod from scratch (attaching another existing one does not work).

This is due to how the crafting requirements are checked. From testing I've found that the game only checks if you meet the requirements for all of the current recipes when you build a mod, and not when you attach a mod. This makes sense from an efficiency standpoint; your perks and how much scrap you have are not changing when you attach a mod so why waste calculations updating requirement checks.

If anyone thinks of a fix for this (e.g. making the game update requirements when attaching a mod, fixing the original bug directly, etc.) please let me know; this has bugged me since the game launched and I'd like to find a way to fix it seamlessly. You could do this in New Vegas for cryin' out loud.

Credits
SKK50 for help with Papyrus