Is the set of pairs of TMs at least one of which accepts the empty word semi-deciable?
Rice's second theorem can be used to show for some sets that they are not semi-decidable, but not the opposite. 

In order to show that this set is semi-deciable, just follow the definition and construct a semi-decider.


   Idea: Simulate both $M_1$ and $M_2$ on $\varepsilon$ simultaneaously using dovetailing. If either one halts and accepts, stop simulating and accept.