I don't have one of those bowls, so I can't go and check for you...... however, you could always try to melt-and-pour a soap into the bowl. If that idea doesn't appeal you can trim a puck of soap with a pocketknife or a vegetable peeler until it fits or even mill soap into your bowl.
I wonder about the same thing. I have a trumper's bowl that I'm hoping to use with another brand soap.
edit: melting triple milled soaps isn't the smartest thing, either. one could melt a col conk soap without much problem (some of the scent might go away)
I think the Trumper's bowl and C&E bowl are very similar in size. I threw my Trumper's bowl away without knowing what I had, but replaced it with a much cheaper C&E bowl on sale. Should have gotten 2!!
EDIT: Yup, the Trumper's products will fit. I took a whiff of my new puck and realized how much scent my open puck has lost. : (
You can squash down a puck of l'occitane cade SS with relative ease in their bowl. I should know, I did so after understanding that my Sienna gave me a rash.