Maintaining wall thicknesses to specification during the casting process can be difficult because of the relatively thin-walled constructions of parts that are cast to include relatively complex internal cooling passageways. The spacing between the core assembly and the surrounding shell is one area that must be controlled to maintain wall thicknesses during the casting process. This disclosure relates to a casting system, and more particularly to a core assembly that may be employed in a casting system to manufacture a part with relatively complex internal cooling passageways. The core assembly for a casting system according to an exemplary aspect of the present disclosure includes, among other things, a core that includes a body and at least one hole formed through the body and a spacer that extends through the at least one hole. The core assembly is composed of refractory metal cores (RMC) and a ceramic core. The spacer is made of platinum or a multi-metal composite. The spacer includes a stud portion and a chaplet portion configured to abut a surface of the body that circumscribes the at least one hole. The chaplet portion is conical. Another spacer includes two studs and a chaplet portion, and the chaplet portion includes a skirt that is positioned between the stud portion and another stud portion. The skirt is conical or rounded. The stud portion includes at least one depth indicator. In a further non-limiting embodiment, the chaplet portion is a bent portion of the spacer. The core is assembled to a second core and is spaced from the second core by a bumper or a second spacer. The core is assembled to a second core or a shell and is spaced from the second core or the shell by a second spacer received in a recess of the second core. The second spacer engages the spacer to sandwich the core between the spacer and the second spacer. The spacer and the second spacer are threadably attached together. In a further non-limiting embodiment, the spacer and the second spacer are riveted together. The casting system according to another exemplary aspect of the present disclosure includes, among other things, a first core and a first spacer received through a hole or within a recess in the first core and that spaces the first core from a shell or a second core. The second spacer is secured to the first spacer to sandwich the first core. The casting system according to another exemplary aspect of the present disclosure includes a spacer assembly, in which a stud portion of one of the first spacer and the second spacer is received through a bore of the other of the second spacer and the first spacer.