The Atlanta Braves are one of a handful of teams that have actively been experimenting with signing relievers and converting them into starters. They shifted Grant Holmes into being a starter and, perhaps most famously, they signed Reynaldo Lopez and moved him into the rotation. Other examples with varying degrees of success around the league include Jordan Hicks, Clay Holmes, Ronel Blanco, Michael King, and Seth Lugo.
It is a tricky blueprint to follow. You have to find relievers that have the attributes you want (miss parts, varied arsenal, no egregious platoon splits) who also have deliveries that won't make their arms explode once given a greater workload.