What is the verb phrase
Many families would have been the proud owners of pet cats and dogs.
Is it would have been?
Right.
Yes, the verb phrase in the sentence is "would have been."
To identify the verb phrase, you can break down the sentence and locate the auxiliary verb (helping verb) and the main verb.
In this sentence, the auxiliary verb is "would" which indicates a conditional or future action. The main verb is "have been," which is a combination of the helping verb "have" and the past participle "been," indicating ownership or possession. When these two verbs are combined, they form the verb phrase "would have been."