He was still unsure as to what the necessities were to create a Personal Fragment. Based on what he was introduced to, a Personal Fragment was something that was created when the remainder of a System within the Host was fused into an object originating from their homeworld.
Technically speaking, a System Slayer was only supposed to have one Personal Fragment. After all, they were birthed in only one world—their homeworld. So, even the notion of having a second Personal Fragment didn't make any sense, much less a third one.
But, since it happened once, Compass Carburettor was of the mind that it could happen again, as long as he figured out the right means to incorporate the laws of the world into himself.
In the Darble World, it was the Dungeon that formed the core of their world's laws. And through obtaining control/ownership of one, he obtained the qualifications to obtain a second Personal Fragment.