In 5e, if a [multiclass](https://open5e.com/characters/advancement.html?highlight=multiclass#multiclassing) character with levels in wizard and cleric wears a [Robe of the Archmagi](https://open5e.com/equipment/magic-items/robe-of-the-archmagi.html) would their cleric spells benefit by the spell save DC and spell attack bonus increase? 

More generally, if you are multiclassed with a class that can wear the robe (sorcerer, warlock, or wizard) and one or more spellcasting classes that could not (bard, cleric, druid, etc.) would the latter classes get the spell save DC and spell attack bonus increase?

Would they get the benefit if they gained the "off-brand" spells through a feat? 

The relevant parts about the Robe is quoted below:

> 
> Your spell save DC and spell attack bonus each increase by 2.
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It does not seem to qualify what class' spells get the bonus.