Learn English – use “needs of the hour” when referring to something plural

In this case it could turn out to be a marketing answer (i.e. how do you want it to sound?)

• an old system and a new system make two systems.

• If the underlying code is basically the same, you could say it's the same system (but you may not want to in the interest of selling the new product)

• If the product is the system (rather than containing it), and you offer two products, you offer two systems (by definition).

Don't forget that a system is a set of interoperable parts, so two independent sets leads to two systems. So I tend to agree with your colleague in this case.

It's not really grammatical number IMO, more logical number, though I agree with the choice of tag.

"spectra" is already the plural; saying "groups of spectras" makes no sense, just as you would not say "groups of dogses" when referring to groups comprising subgroups of dogs.

So, you could say "groups and subgroups of spectra"; otherwise, "groups comprising different sets of spectra" or similar.

I myself have not been able to find any authoritative source that uses "spectra" rather than "spectrum" in the singular in the way that Kris describes. Merriam Webster, for one, has no singular definition for "spectra", although "a spectrum" can be a collective singular - not for a set of spectra, but for colors that make up a continuum; kinds of organisms; frequency or energy in a continuum; a sequence or range of [eg, interests], etc...

EDIT: I delved further:

Google Scholar has a number (though not a large one) of hits for "spectras". However, one use is accompanied by the misspelling "antioxydant"; another has "unusual spectras" in a title but "unusual spectra" in the body; and so on. So there is evidence that "spectras" is getting used, but its use is, at least sometimes, in error. I should think that treating "spectra" only as a plural is, for the time being, the safer option.

EDIT 2:

Google Ngrams shows a negligible use of "spectras" compared to "spectra". Of course, this doesn't account for "spectra" as singular rather than plural, but "spectras" would certainly be in the plural, and evidence just doesn't stack up that it is (yet) standard usage. "Spectrums" use is also low, but it can be seen in this Ngram that it significantly outweighs that of "spectras" as a plural.