Essbase will support the dimensionality than the required but there are performaance implications.
My Recommendation is:
In a BSO application if you are adding more than 7 standard dimensions, recheck again whether it is required or not. Up to 10 some what ok.
Try to eliminate the flat dimensions.
In an ASO application, I have successfully implemented with 17 to 18 dimensions. No issues.
Well it's more likely that you hit the limitation of human brain.
Will you (and/or your customers) really understand what is going on among all these dimensions.
Usually most people already have problems with more then 5-7 dimensions.
Have you asked how they fill the data and even more complicated how whey will retrieve data and still understand what they are speaking to them?
Maybe I'm old fashion but I suspect more then 10 "real" dimension just seems to suggest a lack of case analysis and indicated a approach of first moving hands and then using brain.
The quality and usefullness of a cube does not increases with the number of dimensions...