Is it possible to alter any of Newton's three laws without altering the other two? If yes what will be the consequences? Is it possible to alter any of the newton's laws without altering the other two? (We call such a system as a non-newtonian system)
 A: Searching for "non Newtonian system"  I find only the Newton's law for viscosity of fluids. Then there is the law for gravitation. You must be  talking about the three  laws of motion.
Keep in mind that laws in physics have the strength of axioms in mathematics. They are the "axioms" that allow to relate mathematical equations and solutions to specific observable variables, so as to pick those solutions that fit the data and, important, are predictive, not just a map.
As "axioms" Newton's laws are independent from each other, and could be changed independently, but then the solutions picked and the predictions would be wrong, in the phase space where Newtonian mechanics has been validated.
Take a simple example. In euclidean geometry it is an axiom that two parallel lines do not meet. In spherical geometry "parallel" lines meet, but the euclidean axioms still hold for flat space approximations.
In a similar way, any changes to Newton's three laws should not affect their validity in dimensions where measurements and observations have validated them.
