In Ce-based heavy fermion materials, there is competition between the interactions which lead to a magnetically ordered arrangement of the Ce magnetic moments, and the hybridization between the local moments and conduction electrons, which quenches the local moments and gives rise to a non-magnetic ground state. Sometimes the magnetic transition can be tuned to zero temperature at a quantum critical point (QCP), where unusual properties arise due to quantum fluctuations. CeRh6Ge4 orders magnetically at a low temperature of 2.5 K, but by swapping Si for Ge, the magnetism is suppressed and eventually disappears, likely at a QCP. We propose to examine a series of these doped compounds using muon-spin relaxation so as to characterize the magnetically ordered state, examine how the magnetic state changes as it is suppressed, and to probe the spin fluctuations near the possible QCP.