We've shutout four opponents in a row just twice:
The opening 4 weeks of 2007:
0:0 Columbus, 3:0 Dallas, 1:0 Houston, 1:0 Dallas
May-June 2016:
1:0 Chicago, 7:0!, 3:0 Toronto, 2:0 Seattle
The Toronto and Seattle game sandwiched an Open Cup 1:0 win over Rochester, so that run was really five.