Does OAuth support a 4 legged scenario?

In this four legged scenario, there is a shared service provider, application 1 which holds the consumer data and application 2 which is trying to access data on application 1. How would this scenario look to the user?

My initial thought is that application 2 uses the OAuth 3 legged scenario to get access to the users data with Service Provider. They then use unique account id from service provider to identify user with application 1 and get authorization from application 1.

Anyone solve for this yet or have any recommendations?