Recently, the community has seen a rise in interest and development regarding holographic antennas. The planar hologram is made of subwavelength metal patches printed on a grounded dielectric board, constituting flat metasurfaces. When a known reference wave is launched, the hologram produces a pencil beam towards a prescribed direction. Most earlier works on such antennas have considered only a single beam. For the few later ones that studied multiple beams, they were achieved either by having each beam taken care of by a distinct frequency or by partitioning the hologram, thereby depriving each beam of the directivity it could have had it not shared the holographic aperture with other beams. There have been recent studies related to the use of tensor surface impedance concepts for the synthesis of holograms which have attained control over the polarizations and intensities of the beams. However, this approach is complicated, tedious, and time-consuming. In this paper, we present a method for designing a planar holographic leaky-wave multi-beam metasurface antenna, of which each simultaneous beam radiating at the same frequency towards any designated direction has a tailorable amplitude, phase, and polarization, all without hologram partitioning. Most importantly, this antenna is exempted from the need for the cumbersome technique of tensor impedance. Such features of beam configurability are useful in selective multiple-target applications that require differential gain and polarization control among the various beams. Only a single source is needed, which is another benefit. In addition, effective methods to mitigate sidelobes are also proposed here. Designs by simulations according to the method are herein validated with measurements performed on fabricated prototypes.