More likely we go after (as a minor league FA or small trade) a SS that is blocked or marginalized by his current team in some way (someone 5'8"?) to come in and compete with Ortiz with the hopes of finding gold. Basically, the same as they have done with Collins, Capra, Dunn, Durbin, Vaughn, Perkins, Priester, Bauers, Monasterio, etc...
Not all of them work, but you give yourself another option and at a minimum you push Joey to improve.