Using access token in few browsers at same moment

Hi

I would like to get a user the possibility to access to his Box from a few browsers at same moment. For getting of access to user's Box I am going to use standard OAuth 2. Refresh token is used for getting of access token and then it is used for authorization of requests to Box from browser. There is no problem when one browser is used at same moment. But if two browsers are used then at moment when one of browsers gets new access token the access token gotten and used by other browser becomes invalid. Synchronization of access tokens in a few browsers is not simple. 

What way does the Box API offer for such cases?

(In other similar API getting of new access token does not invalide previous access token, and similar problem does not exists)

Thanks