Need local SEO answer - it's new to me

Can multilanguage site get ranked local in few countries?

Let say I have stores in few countries and want to rank for "store in the city" for all cities I have stores placed.
Is this possible?
Is this possible if I have contact pages different for all places?

(let say) I can proof the address of the stories for g00gle places!

Can't find correct answer nowhere!
Please, help!

It can rank for 'store in the city'.If you can have yourdomain.com/keyword-city and yourdomain.com/city(to add local relevance) pages apart from that,like you mentioned include contact details in both the pages for each city.
And the usual NAP consistent citations.