Is should be a verb phrase?

You're right! "Should" is not a verb phrase by itself. It's actually a modal auxiliary verb.

Here's why:

* Modal auxiliaries like "should", "could", "would", "may", "might", etc., are helping verbs that go before the main verb to express things like possibility, obligation, permission, etc. They cannot stand alone as a complete verb.

To make a complete verb phrase, you need to combine "should" with a main verb:

* Should go

* Should have gone

* Should be going

Let me know if you have any more questions about verb phrases!