We study the “higher algebra” of spectral Mackey functors, which the first named author introduced in Part I of this paper. In particular, armed with our new theory of symmetric promonoidal ∞ -categories and a suitable generalization of the second named author’s Day convolution, we endow the ∞ -category of Mackey functors with a well-behaved symmetric monoidal structure. This makes it possible to speak of spectral Green functors for any operad O . We also answer a question of Mathew, proving that the algebraic K -theory of group actions is lax symmetric monoidal. We also show that the algebraic K -theory of derived stacks provides an example. Finally, we give a very short, new proof of the equivariant Barratt–Priddy–Quillen theorem, which states that the algebraic K -theory of the... category of finite G -sets is simply the G -equivariant sphere spectrum.