>You can also approach someone else at faster closing speed than c if both parties are traveling where the sum of their velocities toward each other is greater than c (like both are going at .6c).

Not true. At relativistic speeds, relative velocity is not a simple addition: https://en.wikipedia.org/wiki/Velocity-addition_formula#Spec...

In your example where both parties are moving at 0.6c towards each other, each will perceive the other to be moving at ~0.88c.