One more-or-less one-step option is to do a CPEC. This is basically splicing by overlap extension (SOEing), but the pieces are all spliced directly into the entire plasmid backbone. You would essentially PCR out the regions in between each mutation, incorporating the mutations into the ends of each PCR product and ensuring that each product has sufficient overlap with the adjacent ones. You then throw all of the purified fragments into a single PCR reaction together with a high-fidelity polymerase, and the pieces act as primers for each other based on the overlap. The polymerase connects them all together (you either PCR out your backbone as a piece as well or just cut it with restriction enzymes and make sure your insert pieces have overlaps at that spot) - transform and you're done! The basic reference here, and another protocol overview here with a link to their specific protocol here.