Hi, i think it depends on the chart you are using... If you want a gauge chart you wont use any dimension, a bar/line chart usually uses 1-2 dimensions, 2-3 dimensions in the grid chart, a pizza chart usually 1 dimension...
There are two limitations: One is the formal number of Dimensions and the other is the memory aspect.
The formal number of dimensions depends on which chart. For example, a bar chart can have 3 Dimensions and 1 Expression (or 2 Dim and several Expr). A pie chart can have 2 Dimensions and 1 expression. But a pivot table can have any number of dimensions and any number of expressions.
The memory aspect is worse. A chart is a cube, which means that the memory usage increases exponentially with the number of dimensions. How many dimensions you can have depends on how many distinct values they have. A simple rule of thumbs is: Never more than 4 dimensions.
To find the largest number of dimensions, you need to understand the concept of "Dimensionality". See Chart Dimensionality.
For example, a bar chart with two dimensions and one measure has dimensionality=2. But the same is true for a bar chart with one dimension and several measures. So basically, you can calculate the dimensionality using
Further, there is a difference between what is possible and what is sensible. The software allows a pie chart with two dimensions and one measure (i.e. dimensionality=2) but in my experience it is not sensible to create such a thing. The user should understand what he is looking at...