Art Unwin wrote:
"The particular case I was referring to was where multiple reflectors
were used to dampen radiation to a maximum."

It works. Taken to an extreme, you have a grid-dish reflector.

Additional reflectors in the plane of the other Yagi-Uda elements don`t
make best use of materials aloft. Placed ahead of the driven element,
additional elements are in a strong field where they may work as
directors to sharpen the forward gain. Placed behind the reflector which
has already reversed most of the energy in its direction, a parasitic
element is less effective as rhere is less energy to work with.

Best regards, Richard Harrison, KB5WZI