Also nuts! Babassu palm, (Attalea martiana, A. oleifera, or A. speciosa), tall palm tree with feathery leaves that grows wild in tropical northeastern Brazil. The kernels of its hard-shelled nuts are the source of babassu oil, similar in properties and uses to coconut oil and used increasingly as a substitute for it. Brittanica.com
You could do an olive oil soap. One ingredient. This will be low lather but you could add sodium lactate to firm it up, some beeswax or stearic also. Some sugar for bubbles.
There is a chart somewhere online that someone made soaps of single oils and it lists all properties. I think it’s on Flickr. Here is some additional soapmaking info
Here is the link. First is the recipe then scroll to see photos how each bar behaves
also this
http://curious-soapmaker.com/big-test-100-one-oil-soaps-part-i.html