First, bosons aren't generally their own antiparticles. Hydrogen is a boson, and can annihilate with antihydrogen, but isn't identical with antihydrogen. It's also possible for fermions to be their own antiparticles, e.g. the hypothesized right-handed neutrinos.

There aren't any special rules governing annihilations. The rule is that any interaction that doesn't violate any conservation laws will happen with some nonzero amplitude (the "totalitarian principle"). In relativistic quantum field theories, there's also a theorem that antiparticles exist with opposite values of all conserved quantities except energy-momentum. That means that if $a$ is some particle and $b$ is another particle with lower (perhaps zero) rest mass, then $a+\bar a \to b+\bar b$ (where the overbar denotes antiparticle) is always allowed. This includes, for instance, $2Z^0 \to 2γ$ or $2π^0 \to 2γ$ which could be called "self-annihilation" of identical bosons. (The $Z^0$ and $γ$ aren't directly coupled, but the totalitarian principle correctly says that the interaction can happen anyway – it's just not very likely.)

First, bosons aren't generally their own antiparticles. Hydrogen is a boson, and can annihilate with antihydrogen, but isn't identical with antihydrogen. It's also possible for fermions to be their own antiparticles, e.g. the right-handed neutrinos in many popular Standard Model extensions.

There aren't any special rules governing annihilations. The rule is that any interaction that doesn't violate any conservation laws will happen with some nonzero amplitude (the "totalitarian principle"). In relativistic quantum field theories, there's also a theorem that antiparticles exist with opposite values of all conserved quantities except energy-momentum. That means that if $a$ is some particle and $b$ is another particle with lower (perhaps zero) rest mass, then $a+\bar a \to b+\bar b$ (where the overbar denotes antiparticle) is always allowed. This includes, for instance, $2Z^0 \to 2γ$ or $2π^0 \to 2γ$ which could be called "self-annihilation" of identical bosons. (The $Z^0$ and $γ$ aren't directly coupled, but the totalitarian principle correctly says that the interaction can happen anyway – it's just not very likely.)

First, bosons aren't generally their own antiparticles. Hydrogen is a boson, and can annihilate with antihydrogen, but isn't identical with antihydrogen. It's also possible for fermions to be their own antiparticles, e.g. the hypothesized right-handed neutrinos.

There aren't any special rules governing annihilations. The rule is that any interaction that doesn't violate any conservation laws will happen with some nonzero amplitude (the "totalitarian principle"). In relativistic quantum field theories, there's also a theorem that antiparticles exist with opposite values of all conserved quantities except energy-momentum. That means that if $a$ is some particle and $b$ is another particle with lower (perhaps zero) rest mass, then $a+\bar a \to b+\bar b$ (where the overbar denotes antiparticle) is always allowed. This includes, for instance, $2Z^0 \to 2γ$ or $2π^0 \to 2γ$ which could be called "self-annihilation" of identical bosons. (The $Z^0$ and $γ$ aren't directly coupled, but the totalitarian principle correctly says that the interaction can happen anyway – it's just not very likely.)

One problem is that if $2a \to 2γ$ is allowed, and $a$'s rest mass isn't zero, then $1a \to 2γ$ is also allowed, which is known as a "decay". The upshot is that there can't be any particles that are stable singly, but annihilate pairwise when you bring several of them together, which may have been what you had in mind. All of this applies whether they're fermions or bosons.

First, bosons aren't generally their own antiparticles. Hydrogen is a boson, and can annihilate with antihydrogen, but isn't identical with antihydrogen. It's also possible for fermions to be their own antiparticles, e.g. the hypothesized right-handed neutrinos.

There aren't any special rules governing annihilations. The rule is that any interaction that doesn't violate any conservation laws will happen with some nonzero amplitude (the "totalitarian principle"). In relativistic quantum field theories, there's also a theorem that antiparticles exist with opposite values of all conserved quantities except energy-momentum. That means that if $a$ is some particle and $b$ is another particle with lower (perhaps zero) rest mass, then $a+\bar a \to b+\bar b$ (where the overbar denotes antiparticle) is always allowed. This includes, for instance, $2Z^0 \to 2γ$ or $2π^0 \to 2γ$ which could be called "self-annihilation" of identical bosons. (The $Z^0$ and $γ$ aren't directly coupled, but the totalitarian principle correctly says that the interaction can happen anyway – it's just not very likely.)