The heavy fermion intermetallic compound URu₂Si₂ continues to attract attention owing mainly to the occurrence of an unknown ordered state at T₀ ~ 17.5 K that is referred to as "hidden order" (HO). HO remains enigmatic, despite more than three decades of research. Tuning studies of chemical substitution, applied magnetic fields, and applied pressure have revealed tantalizing trends in the structural, chemical, and electronic factors that support it. For example, applied pressure and isoelectronic chemical substitutions (Ru → Fe, Os) show unified behavior, where strengthened hybridization between the f and conduction electrons destabilizes HO and replaces it with a more conventional antiferromagnetic order. In contrast to this, chemical substitution that accomplishes hole or electron charge doping is substantially more complex. In order to address how the phases of URu₂Si₂ connect to its chemical analogs and investigate whether similar behavior might occur in other parts of the chemical/electronic phase space, electrical resistivity measurements under applied pressures are performed for the recently investigated chemical substitution series URu₂Si₂-ᵪPᵪ. The T-χ phase space for URu₂Si₂-ᵪPᵪ consists of three regions with the following behaviors: (1) HO is rapidly suppressed towards zero temperature for χ ≲ 0.03, (2) paramagnetism with a heavy-Fermi-liquid ground state for 0.03 ≲ χ ≲ 0.26, and (3) strengthening antiferromagnetic order for 0.27 ≲ χ ≲ 0.5. The results for measurements under applied pressures show that HO is enhanced and converted to antiferromagnetism in region (1), while regions (2) and (3) remain stable against applied pressure. The results for small χ are similar to the parent compound under applied pressure, and the results for larger χ are similar to other electron charge doping series (Ru → Rh, Ir), suggesting there is a connection between all electron charge doping series. Motivated by these results, the chemical substitution series U(Ru₁-ᵪPtᵪ)₂Si₂ is investigated. The T-χ phase diagram is constructed from magnetic susceptibility, electrical resistivity, heat capacity, and high-field magnetoresistivity measurements for arc-melted polycrystalline samples. These measurements show that HO is rapidly suppressed towards zero temperature and abruptly collapses for χ ≲ 0.02. This is followed by a paramagnetic region (0.03 ≲ χ ≲ 0.05), where no ordering is seen down to low temperatures. Magnetic order, with an antiferromagnetic character, emerges and strengthens for 0.06 ≲ χ ≲ 0.19. These results reinforce the connection between the Ru → Rh, Ir and Si → P phase diagrams and suggest that these distinct chemical substitutions provide semiunified tuning in URu₂Si₂ that is likely connected to charge doping. Altogether, these results further constrain the range of viable theories for what is HO. In addition to these studies, improvements are reported on the molten indium metal flux growth technique using an induction furnace for URu₂Si₂ single crystal synthesis, and they are employed to produce single-crystal specimens of UPt₂Si₂.