yes you can. You can use crisco, coconut oil, olive oil, corn.. etc..
vegan soap is nice, it will take awhile to harden depending on the type of oils you use.. but the answer is yes.
Just make sure that some of the oils - crisco type oils in particular - are not blends. If you look at most crisco type oils, they are blendsand formulated differently but the actual crisco is 100% soybean oil. Blends are harder to soap with since you can not tell the amount the oils in it to get an appropriate sap value. Because of this, MMS' calculator won't even give you a sap value but I think Soap Calc will.