To avoid unnecessary complications with isothermal layers and such, let's consider the ISA below the tropopause.
Consider a graph with altitude increasing upwards on the vertical scale and speeds increasing from left to right on the horizontal scale.
The EAS, CAS, TAS and Mach Number can be represented by straight(ish) lines in that order (ECTM) from left to right. The lines fan outwards as altitude increase.
If we rotate the fan slightly so that any one of the lines is vertical, this will show the effect of climbing with that speed constant. For example in constant Mach climb, all of the other speeds decrease as we climb.
VMO is the CAS at which aerodynamic forces start to damage the structure.
Let's consider VMO to be a constant CAS (not quite true but close enough our purposes today).
MMO is the Mach number at which compressibility causes control problems such as Mach Tuck Under. MMO is a constant(ish) Mach Number.
If we fly faster than VMO we damage the structure and if we fly faster than MMO we suffer control problems. So we must never fly faster than either of them
Now lets draw a graph to represent the CAS values equating to VMO and MMO. Our graph will have altitude on the vertical scale and CAS on the horizontal scale.
Because VMO is a constant(ish) CAS we can show it as a straight vertical line.
If we look back at our earlier graph we can see that in a constant Mach climb CAS decreases. So to represent our CAS value for MMO we need a line that is sloping to the left as we move upwards. But where should we locate it on our graph?
At low level the CAS equating to MMO is greater that the CAS equating to VMO. But the speed of sound is related to temperature, so it gradually decreases as altitude increases. So the CAS value for MMO does the same.
This means that MMO is greater than VMO at low altitude, but less than VMO at higher altitude.
So our MMO line should be to the right of the VMO line at the bottom of the graph, but cross over the VMO lone part way up. Our graph should look like an X with the left leg vertical.
Now consider the effects of accelerating from zero at different altitudes. To do this we simply move horizontally from left to right across the graph. At low altitude we will hit VMO before we hit MMO, so we need to watch our CAS.
At the altitude where the two line scross we will hit VMO and MMO simultaneously.
But at high altitude we hit MMO before we hit VMO. So we need to watch our mach Number.
This would all be much easier (and shorter) if I could figure out how to post diagrams, but I have not yet done so!