Local-As-View (LAV) mediators provide a uniform interface to a federation of heterogeneous data sources, attempting to execute queries against the federation. LAV mediators rely on query rewriters to translate mediator queries into equivalent queries on the federated data sources. The query rewriting problem in LAV mediators has shown to be NP-complete, and there may be an exponential number of rewritings, making unfeasible the execution or even generation of all the rewritings for some queries. The complexity of this problem can be particularly impacted when queries and data sources are described using SPARQL conjunctive queries, for which millions of rewritings could be generated. We aim at providing an efficient solution to the problem of executing LAV SPARQL query rewritings while the gathered answer is as complete as possible. We formulate the Result-Maximal k-Execution problem (ReMakE) as the problem of maximizing the query results obtained from the execution of only k rewritings. Additionally, a novel query execution strategy called GUN is proposed to solve the ReMakE problem. Our experimental evaluation demonstrates that GUN outperforms traditional techniques in terms of answer completeness and execution time.