The current method of canning involves using vinegar to "pickle" the foods before boiling. Adding vinegar is required to can low-acid foods such as meats and vegetables, but is not required for canning high-acid foods such as fruits and tomatoes. The following is my recommendation for expanding the canning recipes in-game:
All fruits and tomatoes can be canned using water and sugar and cooking the result.
Vegetables, seafood, and meats can be canned using the current method of pickling (water, sugar, vinegar).
Optionally, if a pressure cooker was added to the game the recipe could forgo vinegar as the higher temperature and pressure would make it unnecessary.
This is a simplification of the canning process for playability. The actual process of canning involves a lot more ingredients and steps.
If the developers wished to expand canning even more, there are a lot of fun things they could add, such as:
Canning fruits in alcohol instead of water
Turning fruits into jams and jellies
Canning salsa's, salads, and soups
Pickled eggs, sauerkraut (from cabbage), and kombucha
Additionally, some method of reusing lids or creating new ones would be appreciated since lids are consumed in the process and are limited in number.