I am a licensed professional engineer (structural) in Toronto and I did my own design for both permitting and construction methodology. So it was free (figuratively speaking).

If I was to be asked to do a design for underpinning a basement my fee would be 10k to 15k which would include hiring a geotechnical engineer to do a borehole and give me a report on the soil I'm dealing with. Drawings would be signed and sealed, suitable for permitting and construction with all specs on the drawings.

As to the cost per square foot, I have no idea. I took a month off work and hired a foreman and two / three pairs of hands and paid them all by the hour. I also laboured / directed with the crew.

Work included new main sewer, new basement drains, some waterproofing, subdrains, excavation, new columns and footings, new concrete floor on 2 inches of SM, vapour barrier, crushed stone subfloor, new water service, plumbing work, and all new electrical panel and associated rewire.

100k to 125k (I didn't keep track of just the underpinning, it was part of a much larger renovation. I kept a spreadsheet of the entire project, which I'm still working on. So my price is an estimate.). Price does not include finishing the basement.

It's a lot of hand digging, staging, pumping of self compacting concrete, etc.