Just note Build ideas are a bit unfinished than Ex-Aid. I actually shouldn't use the word unfinished but it's more like ehh.

Title would be called Kamen Rider Build: Prime Saga, which is a side story towards a new Kamen Rider, Kamen Rider Prime.

Prime will be a single rider. No one will help him out. Just him. Kinda like Kuuga.

I don't have any reason why I named the rider "Prime". It.. just did.

The Kamen Rider Prime name doesn't appear until halfway into the story. More on that later. Before then, he was just another Kamen Rider Build with different fullbottles created by a scientist who secretly worked under Takumi Katsuragi.

Some Bestmatches:

HebiBlade: Hebi and Ken Fullbottles; The main form for Prime's Build form (The Honing Serpent)

HebiKiri: Hebi and Raikiri Fullbottles; The upgraded form of HebiBlade (The Electrifying Serpent)

TreeGeyser: Tree and Geyser Fullbottles (The Scalding Root Riser)

FrogCello: Frog and Cello Fullbottles (The Amphibious Maestro)

MothNimbus: Nimbus and Moth Fullbottles (The Cloudy Monarch)

PhotonLizard: Lizard and Photon Fullbottles (The Lightforth Reptile)

FalcoNeedle: Falcon and Needle Fullbottles (The Soaring Spiker)

JackWorm: Worm and Jackhammer Fullbottles (The Slimy Earth Rumbler)

I do have OilVolcano, HoneyGlue, and MechKiri, but I just realized the fact I don't have any organic bottles in there.

Kamen Rider Leviathan: Another Kamen Rider, named Leviathan, uses the Leviathan Driver. He uses the Leviathan and the Leviathan Fullbottle to transform. The rider design is way different from a usual Build design.

Build can use Leviathan to gain access to Build Leviathan form.

Katsuragi's secret aide, who I'm gonna name him Lars Tobatu (which is a play-on word of Lost Bottle), created booster modules meant to equal in Build's rising power.

The first booster module created was the Prime booster, which was the basis for Kamen Rider Prime. This gave the Build body a new torso armor and arms strength for both sides.

The second booster was the Single Booster, meant to enhance one fullbottle to its full extent. Competes with the FullFullBottle.

Around the half of the series, the obscure Build rider gets a new driver from Lars. It is the Prime driver, which is an upgraded version of the Prime Booster. The body has a Hazard-like appearance, but the details are Brave-like as well. I'm like the only one who'll get it from this design.

This is where Build Prime permanently changes his name to Kamen Rider Prime.

Prime can use the armor parts from different Bottles; they can be interchangeable through the press of a button.

Best Matches in the Prime Driver are called Prime Matches. His usual form is HebiBlade/Kiri Prime.

The Prime Driver uses a Module Core system that allows Evolbottles and Sclashjellies to be used. However, the two are used separately.

Sclash Module: Allows Prime to use Sclashjellies, though it's only exclusive to Sclashjellies. Prime uses the HebiBlade Sclashjelly, which is the first Sclashjelly to have a best match essence in it.

Evol Module: Allows Prime to use Evolbottles alongside fullbottles. This won't give him Prime Matches, but instead Prime Evolutions. His main form is Evol HebiBlade/Kiri Prime. He utilizes the HebiBlade/Kiri Evolbottle and the Prime Rider System Evolbottle to transform (though it says "Rider System").

The body changes to one that looks similar to Kamen Rider Evol's, minus the arms and legs. Prime Evolutions also disable him from Parts exchange, but it's compensated with the sheer power of the Evol system.

He also uses the Scorpion (It says "Sasori") Evolbottle to become Evol Sasori Prime.

Prime Destiny: Prime uses the Destiny Fullbottle to become Prime Destiny, which is his ultimate form. It is created through devotion and the willing to fight for the future when people need him. The bottle is summoned through the Faith (Shinko) and Hope [Kibo] (a reference only I will get XD) fullbottles, causing a Destiny Match to form, summoning the Destiny Fullbottle.

His finisher is the Destiny Finish; activated by pulling the lever three times (it'll say "first chapter", then "last chapter", and finally "Mugen Chapters").

Lars has his Kamen Rider form as well: Kamen Rider Lost. Kamen rider Lost uses the power of the Batta (Grasshopper) Lost Bottle to transform. He has implemented a data absorber system in each of his hands. This'll allow Lars to immediately send data from his hands to a computer in real time.

The driver Lars uses is the Steam Driver, using the same technology from the Transteam and Nebulasteam Gun.

Kamen Rider Youkai

Uses the Youkai Engine and the Youkai Fullbottle to transform. (Probably some rider that appears at the last half of the arc)

Kamen Rider Jockey

Appears in Prime Gaiden, which takes place after the events of Prime Saga. Uses the Jockey Driver with the CD and Mic fullbottles. Any other bottle can't be accessed except those two. However, with the use of the Hazard Trigger, the code for the Driver can be modified to use any fullbottle.

Prime Jockey

Prime uses the HebiKiri Fullbottle and Hazard Trigger to become Prime Jockey. He uses this form until the Prime Driver is usable again.

Gekijouban:

Kamen Rider Hemato: (Hemato is one term for saying blood) Uses the Blood Angel Wing attachment (Sorta like the Magma Knuckle) and the Tenshi Fullbottle to become Kamen Rider Hemato.

I literally made this one up while typing this. Based off Touma from Aquarion.

The movie exclusive items are the Sun and Moon fullbottles and the Eclipse Trigger.

The Sun and Moon bottles can be used by themselves, but will be dangerous if it's with the Eclipse trigger. This is because the trigger isn't fully developed and it needs a user with a high hazard level to master this kind of power.

Of course, Prime masters the Eclipse trigger, which unlocks the full potential of the Sun and Moon bottles.

The Sun bottle has the essence of Black RX.

The Moon Bottle has the essence of Shadow Moon.

The transformation chant for Prime: "Taiyou! Tsuki! Midnight Prime Match! The Aligner of the Sun and Moon! Prime Eclipse!"

Prime Eclipse is a combination of his base form and Hazard armor. Black and White highlights are added on the armor.

And that's pretty much it. Prime does interact with the main world counterparts, but mostly for battle. He has his own story.

In the end he does help Sento out with the final battle, but loses everything (the driver and bottles) as a result of the battle. Then years later Prime battles again with the Jockey Driver, and returns as Kamen Rider Prime, defending the world.

Here's a RideWatch sound: 

When the button is pressed once: "Prime!"

When the button is pressed again: "The lone rider who transforms with a different set of fullbottles is.... Prime!"

When used for Armor time: "Armor time! Prime Match! Prime!!!!!!" 2018 shows on the screen

I should do Ghost OC's then. I kinda lost them because I forgot some forms for the main rider. I think I did more for Ghost than Ex-Aid.