It is not as though Christ emptied himself of something; that is not what Paul actually says.
His actual point is that Christ emptied himself by becoming something that he was not previously, something that, by definition, required humility and ultimately humiliation (Philippians 2:8).
For Christ to make himself nothing, says Paul, was for him to humble himself, and he humbles himself by being born in the likeness of men and by becoming obedient to the point of death.
So, as Paul describes it in this passage, the self-emptying is, in point of fact, a self-adding.
K. Scott Oliphint, God With Us: Divine Condescension and the Attributes of God (Crossway, 2012), p. 118 (HT: DG blog)
Do nothing from selfish ambition or conceit, but in humility count others more significant than yourselves.
Let each of you look not only to his own interests, but also to the interests of others.
Have this mind among yourselves, which is yours in Christ Jesus, who, though he was in the form of God, did not count equality with God a thing to be grasped, but emptied himself, by taking the form of a servant, being born in the likeness of men.
And being found in human form, he humbled himself by becoming obedient to the point of death, even death on a cross.