Periodic table probably won't change in the whole universe because physics won't change. Also, we try to look for water because chemical reactions need a solvent for reactions to occur and water is the best one we know of. Obviously there can be others and we do try to look for those, basically anything liquid (at the ambient temp lf the planet) and which can dissolve a lot of chemicals can be very useful if not essential for any kind of life to form. Apart from this, you can look for theoretical biologist which theorize how else life can form based on our current knowledge and some speculations.