how to combine artifacts of parameterized builds

I have a Build Configuration which builds our software, dependent on parameters in different brandings.

For the deploystep of the software I need to pack a set of brandings together.

So the deploy BuildConfig has a dependency to the buildstep which has to be called several times with different Parameters.

I thougth I could create BuildConfigurations for each branding in a separate Project, which defines the required parameters for the branding and contains a dependency to the buildstep, and then combine the artifacts of these steps in a further BuildConfiguration.

Since parameters are not transfered in dependencies this did not work.

Is there any way to gather artifacts of the same buildstep created with different parameters?