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We present progress on a conceptual design for a new Keck multi-conjugate adaptive optics system capable of visible light correction with a near-diffraction-limited spatial resolution. The KOLA (Keck Optical LGS AO) system will utilize a planned adaptive secondary mirror (ASM), 2 additional high-altitude deformable mirrors (DMs), and ≳ 8 laser guide stars (LGS) to sense and correct atmospheric turbulence. The field of regard for selecting guide stars will be 2’ and the corrected science field of view will be 60”. We describe science cases, system requirements, and performance simulations for the system performed with error budget spreadsheet tools and MAOS physical optics simulations. We will also present results from trade studies for the actuator count on the ASM. KOLA will feed a new optical imager and IFU spectrograph in addition to the planned Liger optical + infrared (λ > 850 nm) imager and IFU spectrograph. Performance simulations show KOLA will deliver a Strehl of 12% at g’, 21% at r’, 53% at Y, and 87% at K bands on axis with nearly uniform image quality over a 40”×40” field of view in the optical and over 60”×60” beyond 1 μm. Ultimately, the system will deliver spatial resolutions superior to HST and JWST (∼17 mas at r’-band) and comparable to the planned first-generation infrared AO systems for the ELTs.