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Members of the CaK(Fe$_{1-x}$Mn$_{x}$)$_{4}$As$_{4}$ series have beensynthesized in single crystalline form and characterized by elemental analysis,thermodynamic and transport measurements. These measurements show that thesuperconducting transition temperature decreases monotonically and is finallysuppressed below 1.8 K. For $x$-values greater than 0.016, signatures of amagnetic transition can be detected in both thermodynamic and transportmeasurements in which kink-like features allow for the determination of thetransition temperature, $T^*$, that increases as Mn substitution increases. Atemperature-composition ($T$-$x$) phase diagram is constructed, revealing ahalf-dome of superconductivity with the magnetic transition temperature, $T^*$,appearing near 26 K for $x$ $\sim$ 0.017 and rising slowly up to 33 K for $x$$\sim$ 0.036. Specific heat data are used to track the jump in specific heat at$T_c$; The CaK(Fe$_{1-x}$Mn$_x$)$_4$As$_4$ data does not follow the scaling of$\Delta$$C_{p}$ with $T_{c}^3$ as many of the other Fe-based superconductingsystems do. Elastoresistivity coefficients, $2m_{66}$ and $m_{11}-m_{12}$, as afunction of temperature are also measured. $2m_{66}$ and $m_{11}-m_{12}$ arequalitatively similar to CaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$. This may indicatethat the magnetic order in Mn substituted system may be still the same asCaK(Fe$_{1-x}$Ni$_x$)$_4$As$_4$. A clear change in $H^\prime_{c2}$($T$)/$T_c$,where $H^\prime_{c2}$($T$) is d$H_{c2}$($T$)/d$T$, at $x$ $\sim$ 0.015 isobserved and probably is related to change of the Fermi surface due to magneticorder. Coherence lengths and the London penetration depths are also calculatedbased on $H_{c1}$ and $H_{c2}$ data. Coherence lengths as the function of $x$also shows the changes near $x$ = 0.015.

Superconductivity and phase diagrams of CaK(Fe$_{1-x}$Mn$_{x}$)$_{4}$As$_{4}$ single crystals