Is specific rotation defined for mixtures of enantiomers or meso compounds?
Nothing stops you from taking the equation and calculating a specific rotation of a mixture. Indeed, as far as I am aware when establishing a new asymmetric reaction, the e.e. is measured by something like chiral HPLC (which will unambiguously give two peaks that can be integrated and compared) while the specific rotation is measured for the resulting mixture of enantiomers as is. So the paper will say something like $99~\%$ yield ($98~\%\ \text{e.e.}$) but below there will be a standard calculation of $[\alpha]_\mathrm D^\pu{20^\circ C}$.

So obviously you can measure a specific rotation of the racemate or meso compound but whatever value you measure should fall into the error of the polarimeter so that the final value of $[\alpha]_\mathrm D^\pu{20^\circ C}=0$.