Stand Synergy is an ability only recently being discovered and experimented with as of The Duality of Stand, though it is likely far more well-known one year later, during The Last Stand.
When two people of blood relation and a close bond use their Stands at the same time, within a close range of each other, and in a way that compliments each other, their Stands become more powerful. This is most notably in regards to their Persistence (a.k.a. Durability) parameter - making them less prone to fatigue and giving their abilities more potency - but also their power.
What counts as "complimentary" is largely up to interpretation, but it needs to be obvious to both participants that the action taken benefits the other. Stand Synergy is also notably able to somewhat change how abilities operate, for example, making Ace of Hearts' normally-straight Lines curl and twist around Sweet Six Shooter's Shots. Depending on the Stands involved, it is possible that an entirely new ability will come into being so long as both Stands maintain contributing their abilities.
Having resentment/anger, or even a general lack of love/affection for one's "Synergy Partner" drastically weakens the Synergy's effects to the point where it may not even be useable, as seen in the fight between Jessie and Matthew Robinson and Josephine and Jacob Joestar.
Notably, Anna Mason's Stand, Scissor Sisters, is somewhat able to use a form of Pseudo-Stand Synergy due to having two bodies, but this is very much not the same thing. Roman Kishibe, after photographing Scissor Sisters, unlocked an ability known as Sisterhood that allowed him to achieve a similar effect to Stand Synergy. Again, however, this is a different, albeit similar, ability.
Josephine Joestar & Jacob Joestar
Jacob can use his stand Ace of Hearts, which can produce laser-like beams of light known as Lines, in tandem with Josephine's stand Sweet Six Shooter's Six Shots. When they use Stand Synergy, Jacob's Line of choice will wrap around Josephine's Shot and will imbue it with a property. When used, the Shot will gain a trim of the same color as the line, as well as a star on the nose. All examples of this so far are as follows:
- Shot No. 4 plus Silver Line made the Shot reflective, causing Jessie Robinson's body that was composed of glitter to reflect it into many smaller copies of itself, destroying her. (Codename: Silver Shot)
- Shot No. 3 plus a Foolish Line imbued with the ability to make things hotter caused the Shot to bounce around, setting everything on fire. (Codename: Flaming Foolish Shot)
- Shot No. 5 plus a Foolish Line designed to make things heavier caused the Shot to fly low circles before drilling through the ground, then erupting upward at its target of choice. It hit hard enough to break bones, and is notably far more durable than Shot No. 5 normally is. (Codename: Heavy Foolish Shot)
- Shot No. 1 plus a Foolish Line that makes things fragile makes the Shot get absorbed into an item. Strangely enough, this actually makes the item nearly indestructible, though when someone picks up the item, it will release a powerful and deadly explosion. Josephine and Jacob left before finding out what happened, so they actually have no idea what the effect of this combination is. (Codename: Landmine Shot)
- Shot No. 4 plus a Foolish Line that makes things sharp, in addition to the Spin present due to Shot No. 4, makes the Shot send out a powerful horizontal shockwave that can damage even Strawberry Fields Forever. (Codename: Shockwave Shot)
- Shot No. 5 plus a Foolish Line that makes things heavily affected by friction results in the Shot quickly beginning to burn up due to air resistance, filling the wind whipped up by the Shot's flight being being set ablaze and filling the area within its patrol with fire. (Codename: Hotshot)
- Shot No. 1 plus a Manic Line creates a Shot that acts as the Manic Line does, punching cleanly through people, with the added effect of now going through Stands as well, and acting as Shot No. 1 does in the sense that it will explode when in contact with a surface. When something is pierced by this Shot, it will soon after begin to glow with rainbow light before being blasted to pieces, even something with an intangible form, like I Still Taste Fire. (Codename: Maximum Destruction Shot)
Strawberry Fields Forever & E.N.I.G.M.A.
By focusing Strawberry Fields Forever's... um... ability... that being power rechanneling, through E.N.I.G.M.A.'s Modern Land, she has the ability to completely override it's normally automatic nature, allowing her to fully control it, its ability, and the nature it creates. This only works while the two are making physical contact with one another.
The control is enough that taking out E.N.I.G.M.A. won't take out his Stand until the control is lifted.
Dianna Sylver & Joseph Sylver
Using Dianna's Stand MARINA's ability to refract phenomena through its body in tandem with Joseph's Stand Oh No!'s ability to replicate and store damage it inflicts through the means of sticker-like marks, the two are able to have phenomena Oh No! comes into contact with be sent away from it and into other things by MARINA. This can range from damage Oh No! inflicts, to Stand abilities such as Ciao!'s magnetism, to even things as powerful as the Spin. This Synergy Ability, since it relies on MARINA's ability, relies on there being sunlight for the two to use.
Jane Kujo & Jotaro Kujo
Jane's stand Cosmic Autumn Rebellion can manipulate the flow of time around certain inanimate (Or plant) object to age or de-age it. However, its true ability is known as Polaris, in which it creates a vibrant aurora that rains down explosions. When combined with Jotaro Kujo's Starman, which allows him to delete objects in exchange for money, it created an effect known as the Rain of Terror, in which CAR's aurora turned red and rained down beams of light that obliterated whatever they touched into nothingness
Roman Kishibe (via Sisterhood)
Roman, after photographing Anna Mason with his Phone, he unlocked an ability known as sisterhood that spawns another phone in his left hand. If he simultaneously uses an ability on both of these phones, it will produce an effect similar to Stand Synergy.
Rest of The Kishibe Family
No. They do not have stand synergy as they have zero affection. If they had stand synergy, I may as well just start handing out requiem arrows. In theory, My Way Anyway, Blueberry Eyes, Done Then Gone, & Wonderwall could synergize, but they won't. Because I have a timeline to maintain.
Kiera Valentino & Caroline Valentino
While no special ability from working together is shown with these two, their stands work in near perfect sync with each other.
Mark Foster & Mia Tyler
These two discovered that they were related mid battle when one of Mark's matches was controlled by Holding Out For A Hero. When this happened, the soulfire had its duration greatly extended as well as turning anyone unfortunate enough to be hit into a ghost while their bodies burned in the fire. (Note: Stand synergy for HOFAH can be used by the rider, despite the fact that the stand is the horse's)
Christina & Alexander
Alexander's Stand Blast Processing allows him to deliver a beatdown several thousand times more powerful than Stands even as powerful as Star Platinum, except for the fact that the beatdown doesn't actually hit for a few minutes. When combined with Christina's Hexacon Forge, it allowed him to deliver the beatdown to a random passerby or to himself and transfer the delayed damage at double strength to someone else who was reflected in Hexacon Forge's shield.
Maxine & Mavis
Mavis's Sweet But Psycho can produce a fine powder that drives people out of their minds with a need to keep being around it. When combined with Maxine's My Head & My Heart, which can multiply emotions by several hundred times, they can fully control a person, seemingly by overwhelming their brain's emotional center. While in this controlled state, a person doesn't have any response to any negative stimuli from either woman, being completely uncaring even if directly attacked by them.
Jessie Robinson & Matthew Robinson
Jessie and Matthew, having very compatible Stands, could in theory be a very powerful synergy duo, if it weren't for the fact that they absolutely despise each other. No synergy ability here.
Mirai Mirror & Downcast Days
Downcasts Days' stand Ocean Eyes allows him to create illusions out of mist as well as form a strange substance known as ectoplasm. Mirai Mirror's Stand Tidal Wave allows her to create literally anything she can imagine, within a few limits. When they works together, Mirai can throw a 'blank patch' at Downcast's illusions and make them real.
Steve & Matthew Milder
If both Abracadabra, which locks a target's heat in place, and Break My Stride, which locks a target's kinetic energy in place, are both active on the same person, both abilities are strengthened and slowly rise in amount.