A while back, Bulbul pointed out to me that in Maltese (the Arabic-derived language spoken in the EU member state of Malta) the plural of "guru" (guru) is "guruwijiet" (where "j"=y.) Obviously, the stem is "guru". The plural suffix is -iet, which is one of the commonest Maltese plurals, and derives from Arabic -āt; compare saltn-a "kingdom" > saltn-iet. But in that case what is the -ij- (ie -iyy-) doing there, and in other cases like omm "mother" > omm-ij-iet? On the face of it it looks like a morpheme without a function.
Oddly enough, as I discussed in my PhD thesis, you get the same phenomenon in Siwi Berber. It happens with Arabic external plurals, eg lə-kdew-a "squash" > lə-kdew-iyy-at, but also with Berber ones, eg ta-ngugəs-t "wagtail bird" > ti-ngugs-iyy-en, baṭaṭəs "potatoes" > baṭaṭs-iyy-ən (the usual plural suffixes are feminine -en and masculine -ən.) You seem to get it occasionally in western Libyan Arabic too (eg žnarāl "general" > žnarāl-iyy-a.)
In both Maltese and Siwi, it appears to be used mainly on nouns whose form is unusual - ones with syllable structures and vowel patterns that are unusual for nouns in the language. The -iyy- suffix looks just like the suffix used to derive nouns indicating origin from a place (eg Sīwi(yy) < Sīw-a); most plural markers in Arabic are specific to nouns of a particular shape, but this suffix can be attached to nouns of any shape. In a sense, it serves as a bridge to reformat the input (the singular) into a form acceptable to the plural function. It thus has a functional value within the context of the morphology. However, it fairly clearly has no meaning at all - which seems fairly remarkable to me. I suppose you could compare the -iss- that shows up in some forms of French -ir verbs (fin-ir "to finish" > nous fin-iss-ons "we finish"), but historically that seems to be part of the stem rather than just an originally meaningless add-on as here.
Can you think of another morpheme (suffix/prefix/whatever) that has to be there in some contexts, but that has no meaning?