Why does sewage back up through our Manchester basement floor drain when it rains hard?

Because roughly half of Manchester drains through a combined sewer, one pipe carrying both sewage and storm water, as the local operators' own city copy states. In heavy rain the combined main runs full, and the lowest opening in the connected homes, the basement floor drain, is where the pressure shows first. That backup is not your lateral failing; it is the city's system surcharging, which is why the home-side answers are a backwater valve on the drain line and a working sump, and why the coverage answer runs through a water backup endorsement rather than the base policy. A backup that happens only in heavy rain is the signature; a backup in dry weather points back at your own lateral.