How many Assumptions can I make in Proof by Induction?

Of course you can! But then you must have two base cases. For example, if you show that ${n=k}$ and ${n=k+1}$ both being true would imply that ${n=k+2}$ is true, and you have two base cases (such as ${n=0}$ and ${n=1}$ for example) then that would imply the case for ${n=2}$ is true. Then it being true for ${n=1}$ and ${n=2}$ would imply it's true for ${n=3}$. Then for $4$, then for $5$... etc etc. It's the same principle