[Cambridge Grammar](http://dictionary.cambridge.org/grammar/british-grammar/as-and-as-expressions/as-as) says:

> 
> **As much as, as many a**s
> 
> 
> When we want to make comparisons referring to quantity, we use as much
>  as with uncountable nouns and as many as with plural nouns:
> 
> 
> Greg makes as much money as Mick but not as much as Neil.
> 
> 
> They try to give them as much freedom as they can.
> 
> 
> There weren’t as many people there as I expected.
> 
> 
> We can use as much as and as many as before a number to refer to a
>  large number of something:
> 
> 
> Scientists have discovered a planet which weighs as much as 2,500
>  times the weight of Earth.
> 
> 
> There were as many as 50 people crowded into the tiny room.
> 
> 
> 

Googling "**plant trees as much as possible**" returns 110K results while googling "**plant trees as many as possible**" only returns 21K.

I would say "**plant trees as many as possible**" is grammatical but "**plant trees as much as possible**" is not grammatical.