No simple answer and I'm not a pilot, but here goes:.
You must have sufficient fuel including reserves (contingency, holding, alternate, enough for a go around etc). these have been discussed elsewhere. You can sometimes push this a bit by en route reclearance - if you are flying from Hong Kong to London you might initially clear to Copenhagen and if you have not used your contingency fuel (typically 3% but that's an oversimplification) to reclear to London.
Ultimately the limit will be the capacity of the fuel tanks. However, that might not leave much payload (possibly only 30,000 in or 135 pax for the 747SP.
Its even more complicated as an aircraft burns less fuel when lighter so you can go further still if you take off at less than the maximum weight.
Also remember that figures stated are for still air. Have a look at the differences between flight times in each direction on FlightRadar24 and you will see the difference. Add in seasonal and day to day differences and you will see that you need a greater range than the great circle distance. Qantas had to offload a lot of passengers on the Perth - London route when faced with abnormal winds..
I saw an aircraft manufacturer (I can't remember if it was A or B) say that they were offering an aircraft with 8,000 nautical miles range but only expected it to be used on 6,000 nm routes to allow for large amounts of freight. A 777 300ER (77W) can accommodate 25 tonnes of cargo in the belly - but not between New York & Hong Kong.
A detailed discussion and charts are are available on the web.
https://bigsynthesis.com/understandi...-range-diagram
The longest distance flight at the moment is Newark - Singapore (15,324 km). According to FR24 the flight on 7 August, a particularly long flight was airborne for 18 hrs 30 mins.
Now for some figures: I was recently reading an M.Sc. thesis on flying from Sydney to London non stop using a 777 200LR. The trip in the winter would take 21 hr 30 min but would require 23 hr 33 min. That looks rather high to me if you allow for reclearing en route but gives an allowance for exceptional headwinds. The weights (based on Jeppeson data) are:
Operating weight empty 144,846 kg
Fuel 145,559 kg
Payload 7,326 kg
Take off weight 297,732 kg
Fuel can be subdivided:
Trip fuel 21 hr 30 - 134,649 kg
Alternate 0 hr 14 - 1,614 kg
Hold....... 0 hr 30 - 2,565 kg
Reserves. 1 hr 19 - 6,761 kg
Total...... 23 hr 33 - 145,559 kg
Apologies - I've not sorted out how the tabbing works
However this is limited by tank capacity. You can add up to three auxilary tanks with an additional capacity of 17,095 kg which is still below the maximum take off weight (347,800 kg). Assuming that half in burnt the payload increases to around 16,000 kg or around 160 souls (say 140 pax). The flight wouldn't take longer but would burn an additional 400 kg / hr owing to the higher weight of the a/c. This would allow a full payload in an all business class configuration.
As I said, I'm neither a pilot or a despatcher and do not have access to flight planning software. Can anyone out there add to this?