Can “could have had to” be possible to use in the past?

Question

We use “have/has to” in the habitual Present-Tense that the subject doesn’t want to do an action willingly.

For instance:

I have to go to the market.

She has to get up in the morning.

So can we use “could have had to” to talk about the past that it was compulsively possible to do the action but I had not to do it?

e.g.

I could have had to go to the market.

She could have had to get up in the morning.

Answer 1

I could have had to go to the market only makes sense in a counter-factual reading:

"[If something-or-other had happened,] I could have had to go to the market [, but in fact that didn't happen, so I didn't have to]".

Could have usually has this sense, whatever other parts of the verb are around.