  We report a pressure study on electron doped SrFe$_{2-x}$Co$_x$As$_2$ by
electrical-resistivity ($\rho$) and magnetic-susceptibility ($\chi$)
experiments. Application of either external pressure or Co substitution rapidly
suppresses the spin-density wave ordering of the Fe moments and induces
superconductivity in SrFe$_2$As$_2$. At $x=0.2$ the broad superconducting (SC)
dome in the $T-p$ phase diagram exhibits its maximum $T_{c,{\rm max}}=20$ K at
a pressure of only $p_{\rm max}\approx 0.75$ GPa. In
SrFe$_{1.5}$Co$_{0.5}$As$_2$ no superconductivity is observed anymore up to 2.8
GPa. Upon increasing the Co concentration the maximum of the SC dome shifts
toward lower pressure accompanied by a decrease in the value of $T_{c,{\rm
max}}$. Even though, superconductivity is induced by both tuning methods, Co
substitution leads to a much more robust SC state. Our study evidences that in
SrFe$_{2-x}$Co$_x$As$_2$ both, the effect of pressure and Co-substitution, have
to be considered in order to understand the SC phase-diagram and further
attests the close relationship of SrFe$_2$As$_2$ and its sister compound
BaFe$_2$As$_2$.
