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(Sc,Ti)Fe₂ Laves phases present a relatively unique case of first-order ferro-ferromagnetic transition originating from an instability of the Fe moment. In addition to large magnetoelastic effects making them potential negative thermal expansion materials, here, we show that Sc_0.28Ti_0.72Fe₂ and related alloys also present sizable magnetocaloric and magnetoresistance effects. Both effects are found substantially larger at the ferro-ferromagnetic transition (<i>T</i>_t1) than near the Curie temperature <i>T</i>_C, yet they remain limited in comparison to other classes of giant magnetocaloric materials. We suggest a strategy to improve these properties by bringing the transition at <i>T</i>_t1 close to <i>T</i>_C, and test its possible realization by Co or Mn for Fe substitutions. The structural and magnetic phase diagrams of Sc_0.28Ti_0.72Fe_2−<i>x</i><i>T_x</i> alloys with <i>T</i> = Mn or Co are explored. Substitutions for Fe by adjacent Mn or Co elements give rise to a breakdown of the long-range ferromagnetic order, as well as a swift disappearance of finite moment magnetism.