Written by Kinoko Nasu with illustrations by Takashi Takeuchi, the visual novel Fate/Stay Night spawned an entire franchise of spin-offs and reinterpretations. Most notably is the highly successful mobile game Fate/Grand Order. Though newcomers may find the series to be inaccessible, the original visual novel (and/or its definitive edition, Realta Nua) or even the prequel series, Fate/Zero, are both great starting points for the series.
The visual novel follows the advent of an ancient mage ritual known as the Holy Grail War, where seven mages each summon seven heroic servants from history or myth to participate in a battle royale. The victor is granted the Holy Grail, said to be an omnipotent wish-granting device. Perhaps the most interesting aspect of the visual novel is its unique plot structure. Much like a game like Fire Emblem: Three Houses, there are three story routes that can be followed, each one focusing on a different heroine.
As such, the closest thing to a direct sequel to the original visual novel has been Hollow Ataraxia, which attempts to combine all three routes. Additionally, it also takes place in the dreamscape of a character who died right before the Fifth Holy Grail War. As such, it is both canon and not canon. However, if a true sequel to Fate/Stay Night were to be made, here's what it would need.
A Fallout With the Mage’s Association
The Mage's Association acts as the ruling body of all mages within Fate/Stay Night. They are an ultra-conservative and mostly self-absorbed lot who prioritize their own legacies. As such, they act as a mildly antagonistic force throughout the series. Their laws and the laws of mage society, in general, create the crux of the conflict between many characters within the visual novel. As such, in a potential sequel, the band of characters -- Shirou, Rin, and Sakura -- would inevitably have to face them.
This is supported by the ending of the third route of the visual novel, Heaven's Feel. In the end, Illyasviel von Einzbern sacrifices herself to destroy the Greater Grail, effectively putting an end to the bloody ritual. Afterward, as the official mage in charge of Fuyuki City, Rin Tohsaka is held responsible and taken to the Mage's Association to stand trial. Though she eventually returns, the ill-will between her family and the Association still stands. Even outside the Heaven's Feel route, the Holy Grail War is still put to a stop by Rin and a mage by the name of Waver Velvet. This means that regardless of which route receives a sequel, the Mage's Association will still have a bone to pick with the central protagonists.
Reconciliation Between Rin and Sakura
It's a shame that this plot point is neglected in both the Fate and Unlimited Blade Works routes because it easily makes for the most emotional moment in all the visual novel. Sakura Matou had the misfortune of being the second child in an esteemed and orthodox mage family, the Tohsakas. As per mage law, only one child may receive the family's teachings. Therefore, in order to "protect" her from living as just an ordinary girl, her father, Tokiomi, gave Sakura away to the Matou family. However, Tokiomi failed to realize that the Matou's training methods were cruel and inhumane. The family head, Zouken, deals in worm magic, using them to store mana and spells as well as feed off of other's mana and life forces. Thus, Sakura's "training" involves her lying in a pit of these worms for sometimes days on end.
Sakura wasn't adopted young enough for her to not remember her old family. She certainly remembers them, however, missing her mother and sister as well as holding deep-seated resentment towards her father. In spite of her generally good nature, she is rightfully bitter towards the world for the way it has treated her. However, the closure of this plot point doesn't come until Heaven's Feel, where Rin finally discovers what her sister has been through, and the two make amends.
This is why in a Fate/Stay Night sequel, the matter of their relationship should be addressed. A sequel with a 2/3 chance of not following up on the Heaven's Feel storyline should address it and confirm that their healing has begun. This would be in character for Rin at the end of the Unlimited Blade Works route since she develops more as a human being through her relationship with Shirou Emiya. It would also be very much in character for Sakura, who becomes friends with Illyasviel at the end of the Fate route; having a friend who can relate to her plight would certainly help develop her confidence.
Additionally, the audience knows that the two still care deeply for one another. As stated previously, if Rin and the other characters take on the Mage's Association, then they will have to engage with Zouken Matou, who survives in every route aside from Heaven's Feel. Essentially, it's both well in Rin's and Sakura's characters to reconnect in a Fate/Stay Night sequel.