How to use different cart template overrides depending on current web domain?

[gba]

Hello all!

VM v3.6.10
Joomla!3.9.19
Mightysites 4.0.4

Having just one shop installation, using Mightysites I display different main products categories depending on the current web domain.

How can I make Virtuemart using different cart template overrides, depending on the current web domain?

i. e.:
'mydomain1.com/cart' shall use template override 'mydomain1_cart.php'
'mydomain2.com/cart' shall use template override 'mydomain2_cart.php'

Thank you very much in advance for any useful hint!

Kind regards,
Gerald