The layered ( = alkali-earth or rare-earth atom, = transition metal, = Sb, Bi) compounds are widely studied for their rich magnetism and electronic structure topology. We provide a detailed characterization of the magnetic and transport properties of , an understudied member of the family. forms with intrinsic Mn vacancies, and we demonstrate that by varying the starting ratio of La, Mn, and Sb, we can synthetically control the Mn occupancy and produce single crystals with . Magnetization and transport measurements indicate has a rich temperature-composition () magnetic phase diagram with physical properties strongly influenced by the Mn occupancy. orders antiferromagnetically at K, where increases with . Below , the phase diagram is complicated. At high , there is a second transition that decreases in temperature as is lowered, vanishing below . A third, first-order, transition is detected at , and the transition temperature increases as is lowered, crossing above near . On moving below , we find the crystal structure changes from the 4/nmm arrangement to an structure with partially ordered Mn vacancies. The change in crystal structure results in the sudden appearance of two new low-temperature phases and a crossover between regimes of negative and positive magnetoresistance when . Finally, we provide powder neutron diffraction for , and find that the high- compositions first adopt a -type antiferromagnetic structure with the Mn moments aligned within the plane, which is followed upon further cooling by a second transition to a different, noncollinear structure where the moments are rotated within the basal plane. Our results demonstrate that is a highly tunable material with six unique magnetically ordered phases, depending on and .