Just to be annoying, I have a palm free recipe which has 35% coconut oil, and most people seem to like it. I know of another another soap maker's award winning recipe which had 45% coconut oil.
The biggest problem I found when developing my recipe was maintaining a good level of bubbliness, and that I found difficult to achieve without reasonably high levels of coconut oil. I liked sweet almond oil in my test recipes, which did seem to improve the bubbles but it is pricey and I didn't want a soap that people with nut allergies couldn't use. The other problem when not using palm is achieving a soap that stays hard throughout use. Though this may just be an obsession of mine.
For what its worth, my no palm vegie soap recipe is 50% olive oil, 35% coconut oil, and 5% each shea butter, cocoa butter and castor oil with 1% sugar added to improve bubbles (standard 5% superfat). It seems to work well enough providing reasonable bubbliness and being fairly long lasting and hardish untill fairly small. I don't find it drying but then I don't have particularly sensitive skin.
If I did it again I might not bother with the sugar and try replacing the castor oil with sweet almond oil (tough on nut allergies!) I have never been convinced about castor oil helping bubbles, though I know some people swear by it. I did do some tests and nobody I asked noticed the difference when it wasn't included. I didn't notice the difference either even when I knew the recipes were different.