Other than “to be”, what verbs in English change in the subjunctive past tense?

The take of CGEL (pp. 87-88) on this is that were is not subjunctive at all, but is its own category, which they call the irrealis were. In particular, there are no other verbs like it, as others have also said.

Irrealis and subjunctive

One striking weakness of the traditional analysis is that it treats the verbs of I be and I were as present and past tenses of a single mood, the subjunctive: this is quite unjustified in terms of the contemporary language. In general they appear in different constructions and are not in direct contrast, but in the one place where it is marginally possible to have a contrast the meaning difference is clearly not one of time but of modality:

[34]  i  If that be so, the plan will have to be revised.        [subjunctive use of plain form]
         ii  If that were so, the plan would have to be revised.                                      [irrealis]

Both are concerned with present time, but [ii] suggests much more than [i] that 'that* is not so. In its normal use, i.e. in modal remoteness constructions, irrealis were does not refer to past time, and there is no synchronic reason to analyse it as a past tense form. Similarly, be is not a present tense form because it has no tense at all, as we argued above on the basis of its failure to undergo backshift in constructions like [27iib] (We demanded that they be reinstated). Moreover, we have seen that there is no inflectional distinction between this be and the ones that occur in the imperative and infinitival constructions. The plain form be, therefore, has no inflectional property of either tense or mood; 1st/3rd person singular were is likewise a non-tensed form, but it does have mood.

The general term subjunctive is primarily used for a verbal mood that is characteristically associated with subordinate clauses with a non-factual interpretation. We are extending the term so that it applies to a syntactic construction rather than a verb-form, but our subjunctive clauses are still characteristically subordinate and non-factual. We need a different term for 1st/3rd person singular were: we call it irrealis, a general term applying to verb moods associated with unreality (i.e. where the proposition expressed is, or may well be, false).

Irrealis category applies only to be with a 1st/3rd person singular subject

The distinction between was and were in [31] [I was very busy. (preterite) vs. If I were less busy I would go with you. (irrealis)] is not sufficient to justify generalising a mood system to all verbs. As we have noted, was is a variant of were in the modal remoteness constructions, so that if we said that took, for example, could be the realisation of either a preterite or an irrealis, there would be no way of telling in cases like [29ii] (If he took the later plane tonight he wouldn't have to rush) whether it corresponded to was or to were, and hence no way of deciding whether it was preterite or irrealis. The encroachment of were into territory normally occupied by was exemplified in [33] [see below] is further evidence that we are not dealing here with a clear case of semantic or syntactic contrast. If we were to say that all verbs had a preterite-irrealis distinction we would be claiming that the massive coalescence of realisational forms that has taken place in the development of English has not produced a change in the system of verb inflection itself, but merely large-scale syncretism. It is much more plausible to say that irrealis were is an unstable remnant of an earlier system - a system which has otherwise been replaced by one in which the preterite has expanded its use in such a way that it now serves to express modal remoteness as well as past time.

For completeness, here is the discussion surrounding the example [33] (p. 87), which was referenced in the segment above. Here '^%' in front of a sentence signifies that what follows is 'grammatical in some dialect(s) only'.

Extended uses of irrealis were

For some speakers, irrealis were is not restricted to the modal remoteness constructions, but is found also in certain backshift and past time uses that bear some resemblance to them:

[33]  i  ^%She phoned to ascertain whether he were dining at the Club   [backshift]
         ii  ^%He looked at me as if he suspected I were cheating on him.     [backshift]
        iii  ^%If he were surprised, he didnt show it.                                           [past time]

In [i] we have backshift in a closed interrogative (the 'original question' was "Is he dining at the Club?"). This construction allows if in place of whether (to ascertain if he were dining…)> and this can be seen as providing a link to the central uses of irrealis were. In [ii] the backshift is in the complement of suspect, which in turn is within a conditional construction (though not, in this case, a modally remote one). Example [iii] is a conditional, but of the open type, not the remote (for a past time remote conditional requires a preterite perfect: If he had been surprised, he would have shown it). Was is much more usual than were in the constructions of [33], and for most speakers probably the only possibility. Were here clearly has something of the character of a'hypercorrection': prescriptive grammar used to insist on were rather than was in modal remoteness constructions, and this may have led to the avoidance of was in certain neighbouring constructions.⁸

^{8Examples like [i] and [iii] are mentioned in some usage manuals, and generally treated as incorrect; but they are found in the writings of highly prestigious authors. Another type of example we have encountered is: The two theoretical extremes of such a scale of formal explicitness would be (a) the case where no information at all were expressed formally, and (b) the case where no information were expressed pragmatically. Were is here in a relative construction embedded within a main clause containing a modal remoteness use of would.}