While doing some research on detergents, I’ve come across some do-it-yourself recipes for making laundry soap, such as this one and one here. Most of these recipes include shaving (or grating) a bar or two of regular handsoap. These approaches seem to be a good way to save a lot of money on laundry detergents. Note that care must be taken with some of the raw ingredients as they can harm the skin and eyes.
I recall coming across in university libraries some very old encyclopedic formularies, for which copyrights have surely expired. These are old recipe books that include a lot of soap recipes. If there is interest, I will find some even more basic soap recipes that do not include bar soap.