We look at the multifractal scaling of fluctuations of the interplanetary magnetic field strength. We analyze the multifractal spectrum in a wide range of heliospheric distances from 7 to 107 AU, including spectra observed by Voyager 1 before and after crossing the termination heliospheric shock. It is worth noting a change of the asymmetry of the spectrum at the termination shock: the spectrum is right-skewed in the outer heliosphere, in contrast to the left-skewed or possibly symmetric spectrum in the heliosheath. We argue that the degree of multifractality falls steadily with the distance from the Sun and is apparently modulated by the solar activity. Our analysis also brings significant additional support to earlier results suggesting that the degree of multifractality of solar wind magnetic turbulence before the shock crossing is greater than that in the heliosheath, where the plasma is in equilibrium, and hence the turbulence may become roughly monofractal.