Notwithstanding Section 20474, a contracting agency may amend its contract or previous amendments to its contract, without election among its employees, to reduce benefits, to terminate provisions that are available only by election of the agency to become subject thereto, to provide different benefits or provisions or to provide a combination of those changes with respect to service performed after the effective date of the contract amendment made pursuant to this section, if the contracting agency has fully discharged all of the obligations imposed by Chapter 10 (commencing with Section 3500) of Division 4 of Title 1 with respect to the contract amendments, and if the amendment provides that:

respect to all members within each of the following classifications: local miscellaneous members, local police officers, local firefighters, county peace officers, local sheriffs, local safety members, school safety members, or all local safety members other than local police officers, local firefighters, county peace officers, local sheriffs, local safety members, or school safety members.

amendment.

Amendments to the contract and amendments of previous amendments to the contract may be effected pursuant to this section only once during any three-year period with respect to each of the classifications.