Multi brand - using variable "modes" as different brands

Recently moved to Figma, and I’m having some headache deciding on how to best structure our files.

We work with a white label app which we brand to (currently) around 20 clients. After moving to Figma, we would love a structure where we have 2 source of truth files (one for iOS and another for Android) which the client files would inherit changes from, but keeping their separate branding (color, radius, fonts). I understand this might not be possible, but is there a good way to avoid having to go back to each client file and manually update components if there are changes to the overall design which affects all client files?

I’ve seen tutorials and examples of multi brand structures where they use Figma Variable “modes”, and set up one mode for each brand. They then link each artboard to a specific mode, so whenever a component is dragged/pasted into that artboard, it inherits the values from that artboard’s linked mode. This is essentially what we would want, but afaik this only works inside a single document. Is this possible across multiple files, while also having client variables stored in their respective files?

How would you tackle this?

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