Elevator with large gravity Battery

Currently lifts (elevators) use counterweight, which acts as battery, in the sense that it stores gravity energy. But it stores energy required for only one upward move of the lift. Whenever lift goes down with people in it, from top to ground, counter weight moves from ground to all the way to top, thus storing energy ( gravity-potential) in the counterweight which now resides at the top. Each downward move of the lift is energy genearting move and each upward move, an energy consuming move. Whenever lift has to be pulled up from bottom to top, this counterweight moves from top to bottom, thus moving lift upward possibly without any electricity at all or minuscale one.

What if it is a residential building and in the morning lot of people are going to ground floor. How we can store all of the energy released in all those SUCCESSIVE downward moves instead of storing just one downwerd move energy.

I suggest, a much larger counter weight, say, 20 times larger. Whenever, lift goes from top floor to bottom, the counter weight moves upward only 1/20th the regular distance.

This arrangement can store energy required for 20 upward moves (from bottom to top) of the lift.

This will require proper gearing.

This is analogous to car hydraulic jack. Small force moves through large distance to move much heavier weight through small distance.