To get two more inches of clearance you will have to go 4" taller than stock tires.
I've seen some pretty good jacked up Vs with a good combination of a body lift and tires.
It the tires rub try a set of hub centric wheel spacers.

 

Stock are about 27.2" in diameter. I have tires that are about 29" in diameter. I have a 2.5" lift. Also, my rims have a different offset than stock. They work great, but they rub a tiny bit when turning. I need to remove the front mudguards and then I think they'll be fine.

That being said, bigger tires do give you a little more ground clearance, but not much unless you do something extreme. A lift will give you better clearance, it doesn't act like a traditional frame lift on a truck - you actually get more suspension and subframe clearance from the lift kits that are available.

 

Won't do a body lift. Just taller tires. Not wider, just taller. Better in snow that way.
Warm weather, taller tires as well.
A body lift does not raise the lowest frame/wheel clearance and it screws up balance for turns & sidehills.

Just looking for the tallest tire that won't rub on bumps or in turns.

 

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I have 215/75-15 on the stock '03 wheels. These are 27.7" tires over the stock 26.3". Not lifted, stock suspension. That would equate to a 0.7" increase in clearance. However, the later year CRV's came on 16" wheels with a 27" diameter tire. Less of a ride height increase for you.

28-29" diameter tires is about as big as you can fit without needing a lift. Like @WelshWonderCRV went into detail on, I'm not a fan of a lift based on the suspension/drivetrain geometry.

 

You can safely do up to a 1.5" suspension lift - not a body lift - without needing to change the subframe spacing. This means more ground clearance on every part of the car, including subframe. It's also incredibly easy. Again, this is different than a body lift.

I did a 2.5" with a 1" subframe drop to keep the geometry safe, which essentially equates to a 1.5" lift in terms of ground clearance to the subframe. Then of course my tires add an additional inch of overall clearance. The car is 3.5" higher, overall.

Regardless, 1.5" has been proven to be the upper safe limit for lifting the 2nd gen CR-V with a suspension lift. Plenty of people have ran it, even using old worn out axles and it articulates very well without any problems - but, in theory, it does speed up wear on the cv joints.

Just letting you know what's available. I totally understand and respect that not everyone is interested in doing this.

 

Hope you realize all of the negatives of 4" taller tires, hub spacers, etc.