a. I don’t think she has seen it, but she may (have).
b. This one needs to be repaired; the other already has (been).
Can you omit the second auxiliary? If so, is it more natural to omit it?
These examples are taken from The Cambridge Grammar (page 100):
Differences between stranding and the central do-support constructions
(a) Stranding not restricted to primary forms
One difference between stranding and the do-support constructions covered in §§2.1.1–3 is that while the auxiliaries in the latter are always primary forms, this is not so with stranding:
 i I don’t think she has seen it, but she may have ___. [plain form]
ii This one needs to be repaired; the other already has been ___. [past participle]
iii %He said I was being unfair, but I don’t think I was being ___. [gerund-participle]
This construction is subject to some regional variation: AmE doesn’t allow [iii], but it does have [i–ii], even if they are less usual than versions in which the second auxiliary is omitted.
The book is saying that it's more usual to omit the second auxiliary in [i–ii]. But I for one wouldn't omit the second auxiliary in [i] or [ii], so I have asked the question. Apparently, @EdwinAshworth seems to agree with me, but others seem to disagree. So I think it's worth investigating in ELU.