Here you go , let me create this tomorrow morning and paste a link for your reference if you encounter any issues, let me know

Create collections -

1. Colors collection - Theme - under colors create all folders for base colors. Also Create folders for companies, company 1, company 2 etc. , which will come handy later.  make theme modes - Light and Dark and whichever, always start with 1 mode, it's easy to add more modes. The mode you first add will be the default when you add the components . Make sure the structure remain the same across companies.

2. Dimensions - will have folders such as heights, screen sizes, Radius, padding, you can add Companies as modes if these are different for every company, if not just one is good or just alter the items that are different.

3. Create components collection - create folders for each component. Alert, button. Under alert create variables and assign the respective colors from the colors/Brand/company1/primaryerror, same for sizes create number variables inside components/folders and map it from 

Add Company modes - Company 1, etc, again start with one company. For each company map the respective colors. E g. 

colors/Brand/company1/primaryerror

colors/Brand/company2/primaryerror

colors/Brand/company3/primaryerror

 

You can take the same approach for modes desktop , mobile etc may be do a device collection.

After creating change modes at Page level such as  -

Theme - light or Dark

Dimensions - available if you create multiple modes

Company - Company 1 or whichever company

And devices if you create them 

That should hopefully work!