Assume a money demand function of the form
$$M^d_t = P_tY_te^{-\theta i_t}$$
where $P_t$ is the price level, $Y_t$ is output, $i_t$ is the nominal interest rate.
Equilibirum in the money market imposes
$$M^d_t = P_tY_te^{-\theta i_t} = M^s_t $$
Forward once, take logs and then differences, to obtain
$$\ln P_{t+1} - \ln P_{t} + \ln Y_{t+1} - \ln Y_{t} = \ln M^s_{t+1} - \ln M^s_{t} +\theta(i_{t+1}-i_t)$$
The difference of logs approximates the growth rate. So the left-hand side is inflation, $\pi_{t+1}$ plus the output growth rate, $g_{t+1}$ and denote $m_{t+1}$ the growth rate of the money supply. Then we get
$$ \pi_{t+1} + g_{t+1} = m_{t+1}+\theta(i_{t+1}-i_{t})$$
The growth rate of the M2 measure for Money in the USA for the period (end-of) 2013-2014 was around $5\%$ (World Bank data). Meanwhile, inflation in the same period fell from $1.5\%$ to $0\%$. GDP growth rate was at $2.2\%$
Then, according to the above relation, we must have had
$$\theta(i_{2014}-i_{2013}) = -2.8\% = -0.028$$
which, given also that the estimates for $\theta$ are below unity, did not happen (it would require a drop in nominal interest rates more than $3$ percentage points, while they were virtually unchanged).
So the equation appears too crude... or, it does open the way to break the money supply into two components, one of which does not affect the price level in an economy.
This won't be a mechanical decomposition: it will require economic arguments in order to single out which of the channels of money supply increase are to be considered "neutral" with respect to the goods price level, and then measure them separately and test empirically this break-up.
For example, the M2 measure that I used above is defined as (World Bank website quote)
Average annual growth rate in money and quasi money. Money and quasi
money comprise the sum of currency outside banks, demand deposits
other than those of the central government, and the time, savings, and
foreign currency deposits of resident sectors other than the central
government. This definition is frequently called M2; it corresponds to
lines 34 and 35 in the International Monetary Fund's (IMF)
International Financial Statistics (IFS). The change in the money
supply is measured as the difference in end-of-year totals relative to
the level of M2 in the preceding year.
By looking separately at the growth rates of demand, time and savings deposits for example, one could start having ideas.