What determines a plane's range? When a planes maximum range is specified, is fuel [capacity] the only constraint or what else is taken into account?

Would it always or ever be the case that a greater fuel capacity will increase range?

Interesting long-flight story of 64 days in the air, but it doesn't get too technical: https://jalopnik.com/how-a-slot-machine-mechanic-flew-150-000-miles-over-64-5971433
As also stated in this answer:

Range is a function of MTOW and empty weight, according to the Breguet Equation for a jet:
$$R=\frac{V}{c_T} \cdot \frac{L}{D} \cdot ln\frac{W_i}{W_i-W_f}$$

with ${c_T}$ = specific fuel consumption, $W_i$ = initial weight, $W_f$ = fuel weight, $L$ = lift, $D$ = drag.

What increases range if other factors remain constant:


Higher speed $V$
Lower specific fuel consumption.
Higher lift/drag ratio.
Higher TakeOff/Landing weight ratio.


The weight ratio can be because of fuel weight used during the flight, but of course chucking ballast overboard helps as well.