"could have" vs. "could have been"

Can somebody explain when to use could have and could have been and under what circumstances? Please explain with an example.

Is it something to do with the active (could have) and the passive voice (could have been)?

I think, if I have understood correctly, that this rule also applies to (would have/ would have been) and (should have / should have been).

Solution 1:

We can use 'could have' to talk about something somebody was capable of doing in PAST but didn't do. (Possible in Past)

I could have gone to Oxford University but I preferred Harvard.
She could have married him but she didn't want to.
They could have bought a house here 20 years ago but chose not to.

We can use 'could have been' to talk about possible present situations that have not happened. (Possible in Present)

I could have been earning a lot as an accountant but the work was just too boring.
He could have been Prime Minister now but he got involved in a big financial scandal.
They could have been the market leaders now if they had taken his advice.

Solution 2:

The former goes with any word. "I could have gone with him" or "I would have gone with her." The latter is just adding a verb to the former, the past tense of to be, which is a linking verb. "I could have been a student" or "I would have been at this place."

TL;DR: The former is just the auxiliaries. The latter is one of the things you can put behind the auxiliaries. You cannot have "could have" alone unless you are using "have" as a main verb and not an auxiliary.