2 domains / 2 retail

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Hi all

Sorry if this is not the right location.

We have 2 retail stores with different names (long story)
I’m sure this probably isn’t possible but could I, using our 1 Shopify store assign the 2 separate domains BUT ... depending on the domain used will result in a different branded store front (but the exact same site)

Example1 .co.uk will land on the site but will be branded as example 1

Example2 .co.uk will again land on the same site only they will see the branding as example 2

Giving myself a headache just thinking about it really.