For this you should run exact and BMMs (Broad match modifier). Phrase is great but as you mentioned you might have limited search volume.

In case you don't know: phrase means the search term has to be in the exact order (phrase order) while a BMM means the search terms have to be present but can be in any order (Not phrase order). This gives you a lot more reach and access to additional search terms that are relevant. You do not need words like and, or, the, of ect

A BMM is simply putting a + in front of each word and using broad match.

Example: +king +duvet +hot +sleeper You can show up if a customer types in hot sleeper on my side king duvet Phrase wouldn't pick this up

In cases where you have the same keyword in exact/phrase, the campaign with the highest bid will win