Before we can discuss the possible alternative extrasolar biological, psychological, theological and societal realities that could exist, we need to establish a framework - if one can even be established. Can more than one kind of "biology" exist? For instance, can there be a planet where life is silicon-based and not carbon-based like here on Earth? Are there universal laws of biology? In other words, what are the limits to the kinds of biologies that can exist? The answer to this will help frame the speculations that will follow.
If we accept the possibility of parallel universes, as predicted by many quantum models of the universe, one answer is that there can exist any infinite number of different biologies since each parallel universe will likely have different physical constants and thus different physical properties. Some universes will be very strange indeed. Some will be impossible for any life to form in - a universe where gravity is too weak, or too strong, for instance. Another complication is the hypothesis that even in our own universe, natural laws and physical constants may not be universal - they may vary from one region of the universe to another.
However, for simplicity sake, let's keep our attention to the region of the universe we find ourselves in. That seems the most pragmatic approach, since it is highly unlikely we will ever be able to see into, let alone venture into, other parallel universes, or regions where our local natural laws and physics no longer are in play.
I would like to propose that there are universal biological laws just as there are universal chemical and physical laws. My reasoning is that biological creatures are composed of biological tissues that are made up of chemicals and are affected by, including making use of, physical laws. Biology cannot be separated from chemistry, nor from physics. If there are universal laws and constants in chemistry and physics, I do not find it a giant leap to say that there are also universal laws and constants in biology.
However, even with those proposed, and yet undefined, universal laws, there are still a dazzling wide variety of biological life forms that can exist. Look at our own planet, from the oxygen and light deprived pressured depths of the sea, to frozen rock in Antarctica, to thin-aired mountain tops, to sun-baked deserts, to lush tropical jungles, life abounds in an incredible array of variety. Looking into our past, we find ever more dazzling array of varieties of all shapes and sizes. While not infinite, and not just any form can exist as a viable creature, the boundaries are difficult to see—that horizon is very far away.
Next—some thoughts as to what some of the universal laws and constants, or constraints, are: Universal Biologies: Order From Chaos.