They sound like cool additions. Vertical expressions definitely seems like the next logical step to expand on the idea. And it would add way more complexity which is good. I could see this becoming a puzzle game where you have to get various rows and columns to equal a target value using the different dice.
You could also do a similar concept to this game with boolean operators. For example '||' is OR. Also in some notations, 'V' used for AND and '^' (upside down V) is used for OR.
Theres a lot you could do with this. Let me know if you end up taking this anywhere, I'd love to see it.