Systems and methods for changing a speed ratio between a compressor boost stage (12) and at least one power turbine (16) of a gas turbine engine (10) are described. Such a system may comprise a coupling device (20) configured to selectively transmit energy from the at least one power turbine (16) to the boost stage (12) according to at least a first speed ratio and a second speed ratio. The system may also comprise an auxiliary power device (22, 26) configured to cause a rotational speed of the boost stage (12) to change from a first speed corresponding substantially to the first speed ratio to a second speed corresponding substantially to the second speed ratio when the boost stage (12) is decoupled from the at least one power turbine (16).