Multifractal analysis of the intermittent solar wind magnetic energy fluctuations reveals new features of the young slow solar wind measured by Parker Solar Probe. The multifractal structure of magnetic fluctuations is analyzed with Rank-Ordered Multifractal Analysis (ROMA) and Partition Function Multifractal Analysis (PFMA). ROMA considers the raw fluctuations at all scales, grouped according to their rank; PFMA provides a multifractal spectrum from a measure extracted from data and assumed to be the result of a multiplicative process. ROMA identifies the bifractal behavior of magnetic fluctuations near the Sun at 0.17–0.19 au, manifesting as quasi-monofractal behavior over two contiguous subranges of inertial-range scales. The bifractality naturally implies the presence of a crossover scale, determined at roughly 100 ion inertial lengths (∼1000 km). The crossover is detected by four different approaches: (1) flatness behavior, (2) structure functions power-law scaling, (3) change of turbulence regime across the inertial range, and (4) change of the ROMA spectra over the two inertial scale ranges. Remarkably, spatial scales of the order of 1000 km have long been shown to be linked to a change in the fractal structure of solar granulation, hinting at a possible effect of solar surface phenomena on the topology of magnetic energy fluctuations close to the Sun. Left-skewed asymmetry of PFMA multifractal spectra further supports the complexity of the underlying dynamics dominated by large fluctuations. Conversely, the lack of right-skewed multifractal spectra at 0.17 au, as detected in the outer heliosphere, underlines the different state of fluctuations near the Sun.