Other factors that affect the supply of money I've read that it is not a hard-and-fast rule that the overall money stock growth rate speeds up in response to an accelerated expansion of the monetary base and a growing money multiplier. If this is the case, what factors unrelated to central bank policy and the lending propensity of commercial banks would cause this theoretical deceleration of money stock growth?
I assume that this question is related to this question on money growth - link to question

The monetary base and velocity completely pin down the wider monetary aggregate. The behaviour of acceleration is slightly trickier, but I will attack it here.

I will firstly use continuous time for simplicity. I will also use my own notation, which is explained.

Let $M$ be whatever wide monetary aggregate you want to study, and $B$ be the monetary base. Velocity $V$ is defined:
$$
V = \frac{M}{B}.
$$
Importantly, this is a definition, and always holds. There is no reason to ascribe changes in velocity to any particular factor, such as preferences of banks.

Then, the rate of change of the money stock is:
$$
\frac{dM}{dt} = \frac{d(BV)}{dt} = B\frac{dV}{dt} + V\frac{dB}{dt}.
$$
Since we are interested in the percentage rates of change, we define growth rates as the time derivative of the variable divided by the variable. That is,
$$
G_M(t) = \frac{\frac{dM}{dt}}{M},
$$
$$
G_B(t) = \frac{\frac{dB}{dt}}{B},
$$
$$
G_V(t) = \frac{\frac{dV}{dt}}{V}.
$$

Then, we see that:
$$ G_m(t) = \frac{B}{M}\frac{dV}{dt} + \frac{V}{M}\frac{dB}{dt}.
$$
Since $\frac{B}{M} = \frac{1}{V}$ and $\frac{V}{M} = \frac{1}{B}$,
$$
G_m(t) = \frac{\frac{dV}{dt}}{V} + \frac{\frac{dM}{dt}}{M} = G_V(t) + G_B(t).
$$
Since you are interested in acceleration, that would be $\frac{dG_M}{dt}$, which is given by:
$$
\frac{dG_M}{dt} = \frac{dG_V}{dt} + \frac{dG_M}{dt}.
$$

In other words, to characterise the acceleration of the money supply, you need to look at the acceleration of the monetary base and the acceleration of the velocity. If we refer back to the question on the money supply in the 1990s, you would have had to calculate the annual percentage change of velocity, and not look at the level of velocity (which is what was displayed).

If we return to discrete time (and observed data are discrete time), the relationships above become approximations. You would have to take the first differences, to get the rate of change, and the difference of the rate of change to get acceleration. For annual data, that means we end up comparing data two years apart, which may break the continuous time approximation.

Since this question asked about other factors influencing the relationship between the base and wider money: there are none. The above equations hold by definition. The question why velocity would change is a more difficult question.