Is it "multi-element" or "multi-elemental"? "Multi-attribute" or "multi-attributed"?

I’ve seen both being used, so I’m having a hard time telling which one is correct. Logic dictates that it’s supposed to be "multi-elemental" and "multi-attributed," considering we have "multicolored," "multiparous," and "multilateral," so you should use –adjective, but then I thought about how we have five-story buildings, three-star restaurants, and the like, in which we have –noun, so that threw me for a loop (and it doesn’t help that there’s an entry for "multielement" in the Merrian-Webster online dictionary).

On a related note, would the answer of this question also apply when multi- is replaced by another term, such as fire- or light- (as in, fire-attributed [or fire-elemental] damage), or is multi- a special case?

Below are some examples, for reference. Rather embarrassing ones, I guess, given the lack of context, but they are the situations I have in mind, in any case.

• He suffered multielemental/multielement (multiattribute/multiattributed) damage.
• That is a fire-attribute/attributed spell.
• A multielement/multielemental (multiattribute/multiattributed) sigil. (In other words, a sigil comprised of multiple elements.)

If it helps, the meaning "element" has in the sentences above is the following (taken from the Cambridge Dictionary):

Earth, air, fire, and water from which people in the past believed everything else was made

And yes, before anyone comments on it, I know that when using "fire," "light," and similar terms, I can just remove -attribute/attributed (-element/elemental) and use those terms directly as adjectives, but I also want to have the option to use them as compound words.