The worst thing Saab could do to the Gripen would be to add more internal fuel, put in a bigger low bypass engine, lengthen the fuselage etc. You would have to completely redesign the wing, fuselage and landing gear to support the larger weight and internal volume.
The empty weight will increase with 300 kg, but the fuselage will remain the same length and other outher dimensions. The landing gear will be different with bígger wheels and brakes.
If Saab wanted a higher performance engine for the Gripen it has a couple options for lower byspass higher thrust designs but it has to seriously consider the consequences of putting in a low bypass engine.
The General electric F404 are fairly reliable but have average power to weight ratio considering its large size. This is because its a high bypass ratio engine by fighter jet standards which gives it fairly average supersonic and high altitude performance. A high bypass design however provides excellent subsonic and low altitude performance for short runways. The F404 is perfectly suited even though its quite old now. The F414 is the perfect step up, its the same size and weight but just runs hotter using new technology to produce more thrust without a reduction in fuel consumption.
Reportedly there has been a number of different engines considered, like the EJ200 and an upgraded RM12. The F414 seems to be the simplest, most low risk choice with a good growth path and it's a no brainer from a technical point that it been chosen. Saab has aid that they are very satisfied with it's fuel economy.
A hot running low bypass F-119 style engine that could fit the Gripen may potentially offer over 50% more thrust while being lighter and smaller than the F404. It would instantly allow the Gripen to supercruise and put it into a whole new class. The down side though is that a low bypass design is less fuel effecient when travelling at subsonic speeds and will reduce endurance. I think this would be a bad thing. This is why passenger aircraft have high bypass engines as they consume very little fuel for the amount of thrust they put out. They are also better suited to subsonic speeds and have poor thrust levels considering their massive size.
Gripen already has supercruise, admittedly not in the F-22 class, and F414 would hopefully increase that.
The demand from the customers seems to be to get longer loiter times, and a relatively high bypass engine is logical. Having a more fuel efficient engine gives more time on afterburner so practical performance would probably be better anyway.
But it's not just a matter of engines, air intakes are also important. If you would combine a relatively high bypass engine with relatively small intakes, couldn't that give the best of two worlds? Good fuel economy at low speed and low thrust, and good thrust at high speed? Granted, for hauling big payloads with high thrust at low speeds it wouldn't be optimal. But Gripen is no bomb truck for deep strikes anyway, it's more geared towards CAS, CAP, maritime patrol and anti shipping. Also with a powerful engine like the F414 it might be quite capable anyway.