Past beam-shaping techniques, developed to transform a Gaussian beam into other waveforms, rely on a wide selection of available tools ranging from physical apertures, diffractive optical elements, phase masks, free-form optics to spatial light modulators. However, these devices – whether active or passive – do not address the underlying monochromatic nature of their embedded phase profiles, while being hampered by the complex, high-cost manufacturing process and a restrictive laser-induced damage threshold. Recently, a new type of passive phase devices for beam transformation – referred to as holographic phase masks (HPMs), was developed to address these critical shortcomings. In this work, we demonstrated the first integration of HPMs into a laser cavity for the generation of arbitrary spatial modes. Our approach allowed for different phase patterns to be embedded into the outputs of a laser system, while preserving the spatial structure of its intracavity beams. The optical system further possessed a unique ability to simultaneously emit distinct spatial modes into separate beampaths, owning to the multiplexing capability of HPMs. We also confirmed the achromatic nature of these HPMs in a wavelength-tunable cavity, contrary to other known passive or active beam-shaping tools. The achromatism of HPMs, coupled to their ability to withstand up to kW level of average power, makes possible future developments in high-power broadband sources, capable of generating light beams with arbitrary phase distribution covering any desirable spectral regions from near ultraviolet to near infrared.