Adding mass to a main sequence star like the Sun would increase its core density and temperature, potentially allowing fusion to occur in both the core and surrounding shell simultaneously. The core is primarily radiative and can change size with added mass, leading to a larger, hotter star. If a hypothetical Sun-sized bucket of water were introduced, it would likely not escape the Sun's gravity and would instead boil off due to the intense heat before reaching the surface. The introduction of such mass could lead to significant changes in fusion rates and luminosity, potentially making the star about 11 times more luminous. Overall, while the scenario is theoretical, it highlights the complexities of stellar physics and mass interactions.