A modular sleeve valve apparatus can include a valve body including a first port and a second port on a first and second sidewall of the valve body. The apparatus can include a first and second valve core sleeved within the valve body. The first valve core can be a cylinder including a first aperture in a cylindrical sidewall and a second aperture in a top base-wall. The second valve core can be a cylinder including a third aperture in a cylindrical sidewall and a fourth aperture in a bottom base-wall. The first and second valve cores can be removable from the valve body and radially rotatable within the valve body. The second valve core can be positioned stacked upon the first valve core to align the second aperture and the fourth aperture.