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Hi,

If you want to express what you did yesterday, I think you would write like this:

I washed my car yesterday.

If you want to add elements of intent, possibility, etc. to the event that might have taken place yesterday, I think you would resort to the use of modals.

I must/should/would/might have washed my car yesterday.

Am I right?

But the use of these forms seems to have limitations in that there aren't any other forms that can be used for the event before that, but instead, the same above modal forms must be used.

I must/should/would/might have washed my friend's car yesterday afternoon during his birthday party, and I must/should/would/might have washed my neighbor's car when I started to leave for his birthday party yersterday morning.
Comments  
If you want to add negative elements of intent, possibility, etc. to the event that might have taken place yesterday but did not, you would resort to the use of modals.

I must/should/would/might have washed my car yesterday.

The use of these forms seems to have limitations in that there aren't any other forms that can be used for the event before that, but instead, the same above modal forms must be used. I don’t agree with you.

I must/should/would/might have washed my friend's car yesterday afternoon during his birthday party, and I must/should/would/might have washed my neighbor's car when I started to leave for his birthday party yesterday morning. This sentence is not properly constructed.
> the use of these forms seems to have limitations in that there aren't any other forms that can be used for the event before that, but instead, the same above modal forms must be used.
I agree that there are not many levels in the past that you can expreess when using "have" with the modals, but your last sentence is awful. Find something better in the literature and come back.
Students: We have free audio pronunciation exercises.
I have learned it is incorrect to write the auxiliary verb 'must' in the past.

I must go to the gym now. [ In 2 hours I am leaving for the gym.]

I must go the gym tomorrow.
Yesterday I had to go to the gym. --> This is correct.

Yesterday I must go to the gym. --> This is incorrect.
Is it fine to say the following?
I must have washed the car yesterday.
BTW, placing too many subjunctive mood forms in the same sentence (as you do in the last sentence) is not recommended. Restrain yourself, if you want to keep clarity to your sentences.
I must have washed the car yesterday, but I don't quite remember.

is correct, but it lacks the obligation of had.
Instead, it shows the probability, meaning:
It's very probable that I washed the car yesterday, but I don't quite remember.

(read Swan, Practical English Usage, must)
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AnonymousBut the use of these forms seems to have limitations in that there aren't any other forms that can be used for the event before that, but instead, the same above modal forms must be used.
Yep, but it's not a limitation, is it? You can express yourself quite well anyway. Emotion: smile
Anonymousthe use of these forms seems to have limitations
Yes. The modals are sometimes called "defective verbs", meaning that they cannot be conjugated in all the tenses available for other verbs. If you need the subtleties of those tenses, you have to switch to some other verb or equivalent expression.

(Recall that a sentence marked with an asterisk * means 'ungrammatical'.)
I must wash the car today. / I have to wash the car today.

*I must wash the car yesterday. / I had to wash the car yesterday.
*I had must washed the car the previous day. / I had had to wash the car the previous day.
I can wash the car today.
*I will not can wash the car tomorrow. / I will not be able to wash the car tomorrow.

CJ