Governs should increase as much of the expenditure on public services as possible.
Would it be correct?
I guess you mean "governments". Anyway, when you write:
Governments should increase as much of the expenditure on public services as possible.
much refers to some quantity of the expenditures. However in
Governments should increase (the expenditures on public services) as much as possible.
much refers to the possibility/chances of increases happening, but not the amount of such expenditures. To make this clearer, you could rephrase it:
Governments should increase as much as possible (the expenditures on public services).
I would avoid splitting up "as much as possible" without a specific reason, as it will be more difficult to understand correctly, especially in speech.
(Replacing governs, a verb, by governments, a noun)
To me, the most natural way of saying this would be:
- Governments should increase expenditure on public services as much as possible.
Even though there is a very slight ambiguity there in whether "much" is referring to the "expenditure" or the "likelihood of the increase", I do not find the other options quite as natural. Especially if you write it this way:
- Governments should increase as much of the expenditure on public services as possible.
it seems to imply a very specific reference to a percentage or fractional increase ('as much of the expenditure'), while statement 1 is more flexible with what kind of a change it is. Mathematically, the two differ, and thus I would prefer/suggest 1. Compared to 2, I could see this statement working better:
- Governments should increase as much expenditure on public services as possible.
but it may sound better or worse than 1 to different people. I guess you could go with 1 or 3. Statement 2 is grammatically correct, but mathematically may not mean what you want it to say. Of course, if that is what you had in mind, though, then 2 (your original statement) works best.