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The term "multiligualism" is generally used to characterize the linguistic capabilities of a single speaker.  If the person uses exactly two (or at least two) languages, they are bilinguial even if no one else in the world is bilinguial.

The term "diglossia" is a socio-linguistic term, it is used to characterize the situation within a society.

If, for the sake of an argument, we assumed that every adult Swiss person is comfortable to use any of Standard Swiss German, French and English, while (perhaps) none of Italian, Romansh, Standard German, or Berndeutsch come anywhere close to that, we could certainly characterize the societal situation as based on universal multilingualism.  This wouldn't, at least not conceptually, prevent the emergence of many examples of diglossia in segments of the multilingual society.

The problem with the purest "multilingualism without diglossia" is that the lack of compartmentalization reduces the incentives for inter-generational transfer of that many languages, so the sociolinguistic situation might not be particularly uniform geographically nor particularly stable over time.  

In simpler terms: if at least one language is completely optional to learn within that particular social group, why even bother to learn it; and if no language is actually optional, that's already diglossia.

I'm sure that you'll find many exciting examples of bilingualism without diglossia, but the best ones will involve pretty small groups[^1], be rather temporary[^2], or be fueled by ongoing language contact or language shifts in adjacent populations.

Diglossia is thus more rewarding to generalize about at a societal level than mere multilingualism and thus currently attracting more of socio-linguistic research.

[^1]: Ideally: individuals.
[^2]: Or greatly shifting in extent, i.e., unstable