Using the Sites module with a multiligual site
You cannot use the PURL "path" method with i18n (Internationalization) because it conflicts with i18n outbound url rewrites - specifically the detection and maintaining of region and language using the path. 

I'm not sure if PURL domain and query string methods will still work. 

I too am looking at this because I have a project where we've used PURL to maintain a brand identifier with the commerce module, but we want to also use i18n in future. I've used i18n and Domain Access modules before, both separately and together and they play well. Domain Access though is not what you want.

My suggestion would be to treat your "set1" and "set2" like regions. The i18n module lets you specify a region and language that is detected from the path. This is so you can have things like 


Germany with German (DE-de)
Germany with French (DE-fr)
Germany with English (DE-en)
United States with Spanish (US-es)
United States with English (US-en)
etc.


So, in these examples we have a country-code and then a language. The i18n module allows you to detect first the country code as a region and the language code for language and then customise the settings based on both. 

I would suggest you use this method to specify custom languages where you have a "set1" for region and a standard language code for language, defaulting to English where no language is defined (ie. LANGUAGE_NONE). 

I'm going to give this a go myself for my project. I'll let you know how I go.