[MalcolmAmos]

Look forward to Scotty's examples ....

I am not sure what you are asking.......

With C F G7 playing as background harmony. I think you are asking -- over the C chord I can only play a C note. Then you ask; "If I wanted to add a 7th, then the background would have to play C7, right?"

EDIT -- ARE YOU BASS GUITAR? Just thought of that, if you are what you are asking fits with the bass guitar. A 1-3-5 or a 1-5 loop over each chord does make since. Now if you are not Bass that would become boring and the following would apply.

Not really. We don't have to be that exact. Without getting too deep here are some of your solo choices - as I see them.

Over C F G7 loop

Any combination of notes from the C Major scale could be played over the entire progression.

Any combination of notes from the C Major pentatonic scale could be played over the entire progression.

Any combination of the C Blues scale could be played over the entire progression.

And you do not have to use all the notes of those scale or play them in any certain order -- play the good ones and leave the bad ones out -- LOL -- sorry about that there are no bad notes as long as you stay in scale, any of them will work.

Much more you could do and I look forward to Scotty's examples. Here is an easy improv "exercise" you might give some thought to.

Start with the C Blues scale. Go up the scale - 6th string to the first string. Then come back down using the C major pentatonic scale (come back down without the blue notes). Back up using the C Major (full 7 note) scale and come home with the C Blues scale.

Then back up using the C Blues scale to the first blue note, jump back to the C note on the 6th string and come forward with another C Blues scale to the second blue note. Come home using whatever you think fits. Mix and match ...... get used to using these three scales and moving between them. Have fun