What two 'fillings' are running concurrently in the present age?
The two concurrent fillings are the filling up of the body of Christ (the calling out of a people for His name) and the filling up of the cup of the iniquity of the Gentiles, or the world in general. They run side by side in the present age.
Les explains that Romans 11:25 says blindness in part has happened to Israel until the fullness of the Gentiles comes in. That fullness is the calling out of a people for His name, the body of Christ. While that body is being filled, another filling runs side by side: the cup of the iniquity of the Gentiles, or the world in general, is filling up. When the body of Christ is full, the period ends, God removes the body, and He picks up where He left off with Israel. Les points to Luke 21 as the setting for this concurrent filling.
And he looked up, and saw the rich men casting their gifts into the treasury.
For I would not, brethren, that ye should be ignorant of this mystery, lest ye should be wise in your own conceits; that blindness in part is happened to Israel, until the fulness of the Gentiles be come in.