Span of roof rafters, how to fix improper structure
I am guessing the big concern comes from the fact there are 2x4's that are 24" on center and that is either old construction or from something else.

Depending on what will reside on that roof (shingles + snow etc..your loading will change) - the 24 inch centers seem to be fine .. now on to the real deal 2 x 4's vs 2 x 6's and the placement.

Using 2 x 6's between the 2x4's will give you that spacing of 2 x 6 on 24 center. So you will have the structural support as if the 2 x 4's were not there - Of course I am assuming you are just adding the same components in 2 x 6's . 
A problem will arise for you when you connect the ridge beam unless it is already a 2 x 6.

As noted in one comment it was recommend you get engineered trusses, so I thought to make sure there is clarity here because my answer depends on your terminology matching - so I included a link to describe. Trusses are faster to install ..
There is a difference in traditional Rafters versus trusses ...

Look here for details:
Differences Rafters and Trusses

Depending on Building codes in your area and the inspectors it might look odd enough that they give you a no pass - even though structurally you might be ok. Weirdness sometimes causes pauses.. 

While I do not see any problems with what your intent is ; except for the Ridge beam connection ....

An old saying I have :

Cheaper to do it right the first time than it is to do it right the second or third time..

If you must disassemble to do it right - Just do it right, you will be GLAD you did.