Methods and apparatus to adjust bleed ports on an aircraft engine are disclosed. An example apparatus for bleeding air from a multi-stage compressor of an aircraft engine includes a compressor case having a plurality of bleed ports. A first bleed port is associated with a first stage of a compressor, and a second bleed port is associated with a second stage of the compressor. The apparatus includes a plenum connected to the compressor case to define a plenum cavity. The plenum fluidly coupling the first and second bleed ports to a fluid conduit for providing bleed air to one or more systems of an aircraft. The apparatus also includes a bleed port selection mechanism located within the plenum cavity. The bleed port selection mechanism including a first portion proximate the first bleed port and operable to prevent fluid flow through the first bleed port.