Traversing Switch Configurations

Peggy is a treasure hunter trying to open two treasure boxes. One box has 2 switches and the other has 4 switches. All of the switches are initially turned off. To open a treasure box,

• she must only change one switch at a time;
• she needs to register every possible combination exactly once.

Peggy successfully opens the box with 2 switches in the following manner:

The sequence in which Peggy toggles the switches

Can Peggy open the box with 4 switches?

Hint: What if Peggy's box had 3 switches instead?