Do multi-layer ceramic capacitor specifications vary within a dielectric class?
The class of a ceramic dielectric tells you a lot less than you think, it only described the temperature coefficient.

Unfortunately, the voltage coefficient is a lot more important these days, with very exotic high K ceramics. 

Manufacturers do use different ceramics with different voltage coefficients for different package sizes even within the same range of capacitors. The reason for this is that as the package shrinks, they tend to increase the ceramic K to allow high values of C to be realised, usually at the expense of voltage coefficient.

If the actual value of minimum capacitance is important, say for stabilising an LDO, then it's imperative to get the longform datasheet from the manufacturer, and stick to a specific value, voltage rating and package size. The shortform data sheet does not usually have the required information.