First, go to the Boeing Airport Planning documents website. This includes a wealth of information about most Boeing commercial aircraft. Choose the document that matches the aircraft you're interested in. I'll choose the 777F document because you mentioned a cargo 777.
Scroll through to PDF page 45. That is a payload-range diagram for the aircraft.
This chart shows the aircraft's capabilities in terms of payload, range, and fuel. The X-axis represents the range. The Y axis represents the amount of payload in terms of OEW (operational empty weight) plus Payload. OEW is used because different airlines outfit their aircraft in slightly different ways, so their starting point (OEW) is different. The 777F's OEW is about 318000lb.
The horizontal line across the top of the payload-range diagram depicts the maximum zero fuel weight (MZFW). This is typically a structural limit for maximum landing weight. You can't land heavier than this without risking breaking the gear.
The first corner of the payload-range diagram represents the maximum gross weight at brake release. In this case, 766,000 lb. I.e. 448,000 lb of payload and fuel. The upper-left corner of this line is the maximum payload choice for that gross weight -- 229000 lb payload, 219000 fuel.
Following along that line, we remove a pound of payload and replace it with a pound of fuel (to maintain constant brake release gross weight). As we do this, the aircraft can reach longer range -- same weight, but more fuel. This continues until the fuel tanks are full. I.e. we reach the second corner on the chart-- 320860 lb fuel.
At that point, we can continue reducing the payload to increase range -- but since we can't add more fuel, we don't get as much of a benefit.
If you wanted to add more fuel tanks in the cargo bays of the 777F, you could do so. The empty tanks would add to the OEW. So instead of starting from 318,000 you might start a few thousand pounds heavier.
To estimate the best achievable range, you want to extrapolate the line from the first corner on the payload-range diagram (the one at constant brake release gross weight). Extrapolate that line out down and to the right until you reach the OEW of your modified aircraft with more tanks. Performing highly accurate eyeball extrapolation, I estimate 13,000 nautical miles.
The slope (m) of this corner of the payload-range diagram represents an important fundamental aircraft performance quantity. We just have to invert it and change the sign...
The slope is (very approximately)
$m=rise / run = -100000 lb / 3000 nm$
Where $SR$ is the specific range of the aircraft. So about 30nm/1000lb fuel. This is a measure of fuel efficiency similar to MPG for a car.
If you look at the term in the front of the Breguet Range Equation, I think you will see the Specific Range there.