Assuming the canopy is supported by fixed base plates, the increase in overturning moment is just (h+4)/h no? Original moment was likely calculated as M=P*l (plus any additional moments due to gravity loads but this shouldn't change overturning unless you are deflecting so much that P-delta affects are large), and now you are calculating M=P*(l+4). Of course your P may increase as the wind constants increase due to height (Ce in Canada) but thats probably pretty negligeable.

Honestly, if you are asking this question, you might want to get some help with this job other than thru the internet.

Quote (jak7)

By what percent the turning moment would increase as a rule of thumb?

A quick and dirty estimate would be related to the percent increase in height. So, the overturning would increase by something like 33%.

(12+4) / 12 = 1.33.

That's a reasonably significant increase. There's no way to know if the existing footing can handle it without doing a more complete investigation / calculation.

Gas station canopies are the first things to fail under high winds. It was probably marginal at best as it was originally designed!

Also, if this is a seismic area and this thing is old you may have other modern code issues relating to cantilever style lateral resisting systems that cause you problems.

Why not add 12'? Go big or go home.