How do I increase max fuel in Mass Effect 3?

Solution 1:

I don't think you can...but you can salvage fuel by scanning ship remains.

Solution 2:

There is no way to increase the Normandy's fuel reserves in ME3. However if you travel around the map you might get a light ping when you hit a certain area (similar noise to when you approach a planet). Actively pinging in close proximity to this hidden planet will reveal a destroyed fuel depot which will give you a one time fuel refill of X amount of fuel. There's usually one in each system. However revisiting this destroyed depot will not refuel you.

WARNING: locating this hidden fuel depot may attract Reapers.