Sainsbury's will limit the number of items shoppers can purchase in a bid to reduce stockpiling, while Morrisons has announced it will create 3,500 new jobs to meet increased demand for home deliveries.
Announcing the supermarket's latest steps, Sainsbury's chief executive Mike Coupe said it "is trying to make sure everyone has access to the items they need"
Moving forward, it will limit shoppers to a maximum of three of any single item, on top of limitations on in-demand products such as soap, toilet roll, long-life milk and pasta.
Supermarkets and government have insisted that the UK's supply chains are well-placed to cope, but have repeatedly urged people not to stockpile.
Sainsbury's also announced measures to protect the most vulnerable people in society, dedicating the first hour of trading to elderly shoppers and giving them priority on home delivery slots.
Mike Coupe added: "[We are] focusing all of our efforts on getting as much food and other essential items from our suppliers, into our warehouses and onto shelves as we possibly can.
"We still have enough food for everyone - if we all just buy what we need for us and our families."
Sainsbury's will also close its cafes and food counters to deploy staff elsewhere in stores.
Aldi too has introduced a cap on all items, limiting shoppers to a maximum of four. Tesco and Boots have also limited purchases on those key items.
Elsewhere, Morrisons is boosting its workforce to cope with the anticipated high demand for online grocery shopping.
It will hire around 2,500 new pickers and drivers, and a further 1,000 staff in its distributions centres. The supermarket will also increase the number of delivery slots available and set up a call centre to help those who do not have access to online shopping.
Morrisons said it was working to help as many people as possible "at a time of national need".
David Potts, chief executive of Morrisons, said: "We expect the days, weeks and months ahead to be very testing and we are determined to do our bit.
"These measures will support our very hard-working colleagues, enable us to provide more food to more people in their homes and create opportunities for people whose jobs are affected by the coronavirus."