Including duplicate tasks in the mining process is a challenge that hinders the process discovery as algorithms need an extra effort to find out which events of the log belong to which transitions. To face this problem, we propose an approach that uses the local information of the log to enhance an already mined model by performing a local search over the potential tasks to be duplicated. This proposal has been validated over 36 different solutions, improving the final model in 35 out of 36 of the cases.