Really big panniers and other baggage
I do the supermarket run every week by bicycle - have done for about 7 years

Family of four so I more or less fill a full size shopping trolley every time.

This is made possible by a Christiana Trailer which is pretty much equivalent in load capacity to a shopping trolley:



I have a bike that is now dedicated to the role of towing this beastie (for the supermarket run and for the Saturday morning run to the Greengrocer and the Butcher). Would only give it up for an actual cargo bike/trike