A modular hydraulic intensification system includes a housing configured to be deployed within a subsea landing string. The modular hydraulic intensification system also includes multiple hydraulic intensifiers positioned within the housing, wherein each hydraulic intensifier includes a first chamber configured to fluidly couple to a hydraulic fluid supply and a second chamber configured to fluidly couple to one or more landing string valves within a lower portion of the subsea landing string. The modular hydraulic intensification system further includes a shuttle valve fluidly coupled to the respective second chambers of the multiple hydraulic intensifiers, wherein the shuttle valve is configured to enable flow of an output fluid across the shuttle valve from the respective second chambers of the multiple hydraulic intensifiers and to block backflow of the output fluid across the shuttle valve toward the respective second chambers of the multiple of hydraulic intensifiers.