The following trick requires Stun Grenades (found in the back of the room with Boss 3), Blood Test Kit (found in the same room), and the Grenade Launcher (in the save room down the hall from Boss 3). Starting after third Boss fight (hanging tentacle monster), backtrack your way out of the weapons lab, back up the air vent, and to the "mine" elevator. As soon as you reach the surface, strafe left, and equip both the Grenade Launcher and Stun Grenades. If you step forward at all, it triggers an intermission sequence you have to die and start the level over. Enter first person mode and aim up the corridor, parallel with the bottom of the last metal wall panel. Launch a grenade and quickly walk forward. The intermission sequence will trigger, but Whitley will stand still instead of running off. Now, quickly run ahead of him (preferably block his path to slow him down) and use the Blood Test Kit. He now trusts you enough to follow orders. Order him to follow you (otherwise he walks around the corner triggering guards to attack) and give him a weapon. You have now backup. He only lasts a brief amount of time, and will disappear roughly halfway up the snow corridor, which appears scripted. However, every bit of backup firepower helps in that spot.
In the last level where you have to find Whitley as an objective, as you stand in the elevator strafe left and launch a grenade just outside the opening. If done correctly, you can bring Whitley with you to help kill all the troopers. Note: You have to give him some weaponry.