DyMn$_2$O$_5$ is an intriguing multiferroic material showing multiple magnetic, electric and structural transitions. We present here the systematic study on the effect of Sr doping at the Dy site of DyMn$_2$O$_5$ through magnetic and dielectric measurements. Doping of divalent Sr at the Dy site is expected to enhance the Mn$^{4+}$:Mn$^{3+}$ ratio and it will also dilute the Dy site. Our study indicates large enhancement in the magnetic anomaly observed close to 43 K, which we believe to be related to the increased ferromagnetic correlations on Sr doping. Gradual increase in coercive field at 3 K with the Sr doping and decrease in bond length of adjacent Mn$^{4+}$ ions further support the enhancement of ferromagnetic corelations in the system. The parent sample shows a large magnetocaloric effect around 12 K, the magnitude of which found to decrease with increasing Sr concentration. The doping also enhances the anomaly at around 28 K observed in the dielectric permittivity versus temperature data, and this anomaly was earlier claimed to be associated with the spin reorientation as well as a simultaneous transition from one ferroelectric state to other. The electric orderings observed below 25 K are found to be susceptible to the applied magnetic field, and supports the view of Ratcliff II {it et al.}(Phys. Rev. B {bf 72}, 060407(R)(2005)) of concomitant changes in the magnetic structure associated with the multiple electric transitions.
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