Can you add any words after keep and be? What are the different meanings of adding different words? What's the difference between these two words?

To compare keep and be together here, we can only compare their usage as a copula. As a copula, be has a wide range of parts of speech.

He is a student. (noun as predicative)

He is very anxious. (Adjective as predicative)

They're out. (Adverb as predicative)

We are in Grade Two (prepositional phrase as predicative)

This movie is very touching. (The participle is predicative now)

They are excited about the news.

His dream is to be a scientist.

One plus two equals three. (Numbers as predicative)

When keep is a semi-verb, it is only predicative with adjectives.

Keep quiet.

However, the object complement after keep can use different parts of speech, but the infinitive of verbs cannot be used as the object complement of keep.

Keep the room tidy (adjective as object complement)

Don't shut him out (adverb as object complement)

Keep a secret. (Nouns as object complements)

Put the jar in the shade. (Preposition phrase as object complement)

Don't keep me waiting too long.

Keep us informed (past participle as object complement)