Should and were to can also be used in the if-clauseA group of related words containing a subject and a verb. of third conditional sentences. To express that the sentence refers to past, however, a perfectThe aspect expressing completion. E.g.: He’s finished university. infinitive is used after them. Note that this usage (like the situation it expresses) is not very common.

When reporting a third conditional, we apply no tenseA grammatical category that is marked by verb inflection. To express when an event or action happens in time or when a state exists, we use tenses. changes.

"If they had been more careful, they wouldn't have been killed in the accident", the policeman muttered.
The policeman remarked that they wouldn't have been killed in the accident if they had been more careful.

When reporting a second conditional, the following tenseA grammatical category that is marked by verb inflection. To express when an event or action happens in time or when a state exists, we use tenses. changes may be applied.

When reporting a first conditional, the following tenseA grammatical category that is marked by verb inflection. To express when an event or action happens in time or when a state exists, we use tenses. changes may be applied.

When reporting a zero conditional, the following tenseA grammatical category that is marked by verb inflection. To express when an event or action happens in time or when a state exists, we use tenses. changes may be applied.

The rules that apply here are essentially the same as those discussed on the previous pages, that is, tenseA grammatical category that is marked by verb inflection. To express when an event or action happens in time or when a state exists, we use tenses. and modal changes occur if the reported sentence is out of date at the timeA concept which is related to our perception of reality; that part of existence which is measured in seconds, minutes, hours, days, weeks, etc. of reporting. Note that, even in this case, some tenses and modals do not change.

I would prefer it if it stopped snowing.

This is a second conditional sentence.

I’d prefer to stay at home instead. (= I’d rather stay at home.)
I’d prefer to have gone by tram. (= I’d rather have gone by tram. /  I’d be happier if I had gone by tram.)

Note the difference between the sentence above and this one:

subject 1 + would rather/sooner + clause (subject 2 + past perfect)

I’d rather we had never met. (= If only we had never met.)
What would you rather I had written? (= What do you wish I had written?)

subject 1 + would rather/sooner + clause (subject 2 + unreal tense)