The first sunday of the month, as stated on the official Minister of Culture's website, the entrance to the museums and the italian archeological state parks is free.
In the days of free entry you cannot make any reservation and the priority of entry will be only for people with disability and pregnant women.
For Michelangelo's Secret Room the booking online or via call center will remain mandatory even in days of free entry. However in these dates you will not have to pay any fee of reservation.