Should I perform a disjunctive syllogism directly on three expressions simultaneously?

$$\quad\quad \quad \;\;\;\;\;\;1. \quad \lnot R \lor \lnot T \lor U$$ $$2.\quad R$$ $$3. \quad T$$ $$4. \quad U $$

Given the three premises $(1), (2), (3)$, yes indeed, $(4)$ is true. But assuming your task is to prove that $U$ follows from the first three premises: why wouldn't you add the intermediate step $(3.5)$, citing the premises and/or derivations used?:

$$(3.5)\; \lnot T \lor U\tag{ (1) (2) Disjunctive Syllogism}$$ $$(4)\; U \tag{ (3), (3.5) Disjunctive Syllogism}$$

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You may want to speak to your instructor about how much detail to show. The disjunctive syllogism is typically taught as:

$$p \lor q$$ $$\lnot p$$ $$\therefore q$$

so you may also need to add $\lnot\lnot R$ from $(2)$, and $\lnot\lnot T$ from $(3)$, and then move to what I've numbered as $(3.5), (4)$, citing the respective premises to which double negation applies.

Again, it depends on your instructor, how explicit you need to be in your proofs.

Given:

$$1. ¬R∨¬T∨U$$ $$2. R$$ $$3. T$$ $$4. U$$

Using parentheses:

$$1. ¬R∨(¬T∨U)$$

Disjunctive syllogism is: $$p∨q$$ $$¬p$$ $$∴q$$

Next step:

$$1. ¬R∨(¬T∨U)$$ $$2. R$$ $$3. T$$ $$4. U$$ $$5. (¬T∨U) //justification: 1,2 DS $$ $$6. U //justification: 3,5 DS $$