We report the growth and characterization of ${\mathrm{MnPd}}_{5}\mathrm{P}$, a rare-earth-free ferromagnet, with ${T}_{C}\ensuremath{\approx}295\phantom{\rule{4pt}{0ex}}\mathrm{K}$ and planar anisotropy, and conduct a substitutional study with its antiferromagnetic analog ${\mathrm{MnPt}}_{5}\mathrm{P}$. All compounds in the family adopt the layered anti-${\mathrm{CeCoIn}}_{5}$-type structure with the space group $P4/mmm$, and EDS and x-ray diffraction results indicate that ${\mathrm{MnPt}}_{5}\mathrm{P}$ and ${\mathrm{MnPd}}_{5}\mathrm{P}$ form a complete solid solution. Based on measurements of the temperature- and field-dependent magnetization and resistance, we construct a temperature-composition ($T\text{\ensuremath{-}}x$) phase diagram for $\mathrm{Mn}{({\mathrm{Pt}}_{1\ensuremath{-}x}{\mathrm{Pd}}_{x})}_{5}\mathrm{P}$ and demonstrate that the essentially antiferromagnetic order found in ${\mathrm{MnPt}}_{5}\mathrm{P}$ is extraordinarily sensitive to Pd substitution. At low Pd fractions ($x<0.010$), the single antiferromagnetic-like transition in pure ${\mathrm{MnPt}}_{5}\mathrm{P}$ splits into a higher-temperature ferromagnetic transition followed first, upon cooling, by a lower temperature ferromagnetic to antiferromagnetic transition and then by a re-entrant antiferromagnetic to ferromagnetic transition at even lower temperatures. The antiferromagnetic region makes up a bubble phase that persists up to $x\ensuremath{\approx}0.008$--0.009 for $T\ensuremath{\approx}150\phantom{\rule{4pt}{0ex}}\mathrm{K}$, with all samples $0\ensuremath{\le}x<0.008$ recovering their initial ferromagnetic state upon further cooling to base temperature. Once $x>0.010$, $\mathrm{Mn}{({\mathrm{Pt}}_{1\ensuremath{-}x}{\mathrm{Pd}}_{x})}_{5}\mathrm{P}$ undergoes a only single transition into the ferromagnetic phase. The Curie temperature initially increases rapidly with $x$, rising from ${T}_{C}\ensuremath{\approx}197\phantom{\rule{4pt}{0ex}}\mathrm{K}$ at $x$ = 0.013 to a maximum of ${T}_{C}\ensuremath{\approx}312\phantom{\rule{4pt}{0ex}}\mathrm{K}$ for $x\ensuremath{\approx}0.62$, and then falling back to ${T}_{C}\ensuremath{\approx}295\phantom{\rule{4pt}{0ex}}\mathrm{K}$ for pure ${\mathrm{MnPd}}_{5}\mathrm{P}$ $(x=1.00)$. Given that Pt and Pd are isoelectronic, this work raises questions as to the origin of the extreme sensitivity of the magnetic ground state and the nature of the re-entrant ferromagnetism at dilute Pd levels.