Is cart share is possible for multi language multi domain setup?

I have english and french store setup by a single instance of vsf and vsf-api. Each language is working on separate domain ( like for english http://english.local and for french http://french.local ). But cart share in not working for non-logged in user between these stores. ( if a non-logged in user add some items to cart on english store and moved to french store cart get empty; in the same way user logged in on english store need to re-login on french store ).
As I look into the local.json file of both ( vsf and vsf-api ), there is no configuration settings for this.
Is it possible to share cart and logged-in user in multi language multi domain setup?
Store codes are sending in response header to each domain.