When you say "relative estimates," I assume that you mean relative risk estimates. If so, then you can do this with the NLMeans and RunBY macros. See this note that shows how you can add LSMEANS and STORE statements in PROC LOGISTIC followed by the NLMeans macro to obtain relative risk estimates from a multinomial model. To do this for each of your multiple imputations, you will use the RunBY macro to run the NLMeans macro repeatedly over the imputations. You can then combine the relative risk estimates using PROC MIANALYZE. This is discussed and illustrated in the NLMeans macro documentation. See "Analysis of imputed data" in Example 2 in the Results tab of the macro documentation.
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