This paper aims to improve the efficiency of unsat coreguided MaxSAT solving on a sequence of similar problem instances. In particular, we consider the case when the sequence is constructed by adding new hard or soft clauses. Our approach is akin to the well-known idea of incremental SAT solving. However, we show that there are important differences between incremental SAT and incremental MaxSAT, where a straightforward implementation may lead to a sharp decrease in performance. We present alternatives that enable to cope with such issues. The presented algorithm is implemented and evaluated on practical problems. It solves more instances and yields an average speedup of 1.8× on previously solvable instances.