If 100 machines play fair, >50% requires 101 evil machines, but >60% requires 151 evil machines.
An honest network participant will accept the chain with the largest accumulated proof of work. This is necessary to resolve forks of the chain, which are a natural occurrence.
A 51% attack means that the attacker can create a chain with more work than the rest of the network.
The idea that you can say "we require 60%" makes no sense by itself - you have to say what you actually mean in the context of a competitive and adversarial distributed proof of work blockchain network...
Maybe you have some ideas how to avoid history-rewriting attacks, in which case you should write a white-paper and launch your own sh1tcoin or ICO (only half joking).
Some blockchains require a higher amount of consensus to fork (blockchain fork).
For others who might be confused, here is a good resource:
https://bitcoin.stackexchange.com/questions/26999/supermajor...