Maybe I did not make myself understood
MatthewAllen asked

we're moving the speed of light
And another galaxy is too
and we're going the opposite direction?
Does the relative speed limit hold?

I supposed MattheewAleen meant

If we are driving on the motorway and an other car is moving towards us at the same speed, then the other car is moving towards us at a double speed

Is it the same situation in case of a galaxi moving at the speed of the light towards the earth ?

Forget for a while the expansion of the universe
The answer is negative
The galaxi can not exceed the speed of the light

Why ?

Claiming ;
My car is driving at the speed : my.speed
The other car is moving at the speed : you.speed
It is implicit that we refer my.speed and you.speed to the same coord system :
The earth
In other words we can define :
- two relative coord system (the cars)
- one absolute coord system (The earth)

The question is :

Can we extend this concept to the whole universe ?

Common sense and and Newton say : yes, in theory it is possible


Einstein said : no, it is not possible neither in practice nor in theory

If MatthewAllen claim

The galaxi is moving at the speed...

Einstein would ask him

What coord system are you referring to ?

According to the theory of relativity only local coord systems make sense
It is not possible to define an absolute coord system

Same consideration as far as time is concerned