The design and practical realization of composite materials that combine fluidity and different forms of ordering at the mesoscopic scale are among the grand fundamental science challenges. These composites also hold a great potential for technological applications, ranging from information displays to metamaterials. Here we introduce a fluid with coexisting polar and biaxial ordering of organic molecular and magnetic colloidal building blocks exhibiting the lowest symmetry orientational order. Guided by interactions at different length scales, rod-like organic molecules of this fluid spontaneously orient along a direction dubbed "director," whereas magnetic colloidal nanoplates order with their dipole moments parallel to each other but pointing at an angle to the director, yielding macroscopic magnetization at no external fields. Facile magnetic switching of such fluids is consistent with predictions of a model based on competing actions of elastic and magnetic torques, enabling previously inaccessible control of light.iquid crystals (LCs) that combine fluidity with many forms of orientational and partial positional order are ubiquitous (1, 2). Fluids with polar ordering were envisaged by Born a century ago (3-5), with their study recently guided by prescient theories of Brochard and de Gennes (6-12). An experimental search for small-molecule biaxial nematic fluids has gone on for decades (2, 13). Many types of low-symmetry ordering have been found in smectic and columnar systems (14, 15) with fluidity in only two and one dimensions, respectively (1). However, nematic LCs with 3D fluidity and no positional order tend to be nonpolar, although phases with polar and biaxial structure have been considered (15)(16)(17). In colloids, such as aqueous suspensions of rods and platelets, nonpolar uniaxial ordering is also predominant (1, 18). At the same time, there is a great potential for guiding low-symmetry assembly in hybrid LC-colloidal systems, in which the molecular LC is a fluid host for colloidal particles (18). Different types of LCmediated ordering of anisotropic particles can emerge from elastic and surface-anchoring-based interactions and can lead to the spontaneous polar alignment of magnetic inclusions (6), although the orientations of the magnetic dipoles of colloidal particles were always slave to the LC director n, orienting either parallel or perpendicular to it without breaking uniaxial symmetry (6-12).In this work, by controlling surface anchoring of colloidal magnetic nanoplates in a nematic host, we decouple the polar ordering of magnetic dipole moments described by macroscopic magnetization M from the nonpolar director n describing the orientational ordering of the LC host molecules. The ensuing biaxial ferromagnetic LC colloids (BFLCCs) possess 3D fluidity and simultaneous polar ferromagnetic and biaxial order. Direct imaging of nanoplates and their magnetic moment orientations relative to n and holonomic control of fields that strongly couple to M and reveal their orientations, as well as numer...