A few initial thoughts, as this is a new topic to me.
I am inclined to agree that universals do not have any kind of supernatural existence in a non physical / temporal realm. They also don't "exist" in time and space in terms of being something we can point to, because if that were the case they would be particulars.
But, as we saw in the previous modules, we can talk about things that don't exist in space and time in a meaningful way, and so they must have some kind of subsistence.
My initial reaction, having thought about how I would describe universals, is that they seem to be (or at least have their origin in) some kind of "rule" for describing things (either properties or relations).
We can all understand what someone means by "higher" or "redder". These are terms which help us to talk about particulars, and to understand what we mean when we want to convey complex ideas. So the universal "red" is a rule which allows us to ascribe a subjective sense experience (or perhaps a particular wavelength of light).
The universal "red" only seems to be of use in communication of some form. Without communication I'm not sure that universals serve much purpose.