We performed systematic studies of the combined effects of annealing/quenching temperature (TA/Q) and T=Ni, Rh substitution (x) on the physical properties of Ca(Fe1−xTx)2As2. We constructed two-dimensional, TA/Q-x phase diagrams for the low-temperature states for both substitutions to map out the relations between ground states and compared them with that of Co substitution. Ni substitution, which brings one more extra electron per substituted atom and suppresses the c-lattice parameter at roughly the same rate as Co substitution, leads to a similar parameter range of antiferromagnetic/orthorhombic phase space in the TA/Q-x space as that found for Co substitution, but the parameter range for superconductivity has been shrunk (roughly by a factor of 2). This result is similar to what is found when Co- and Ni-substituted BaFe2As2 are compared. On the other hand, Rh substitution, which brings the same amount of extra electrons as does Co substitution, but suppresses the c-lattice parameter more rapidly, has a different phase diagram. The collapsed tetragonal phase exists much more pervasively, to the exclusion of the normal, paramagnetic, tetragonal phase. The range of antiferromagnetic/orthorhombic phase space is noticeably reduced, and the superconducting region is substantially suppressed, essentially truncated by the collapsed tetragonal phase. In addition, we found that whereas for Co substitution there was no difference between phase diagrams for samples annealed for 1 or 7 days, for Ni and Rh substitutions a second, reversible effect of annealing was revealed by 7-day anneals.