Super Saiyan Blue Kaio-ken is an amalgamation form utilized by Goku during his battle against the legendary assassin Hit. First Goku transforms into Super Saiyan Blue. After which he performs his Kaio-ken technique while he is still in his SSB form. The resulting combination creates a unique dual aura. An outer shell of dark scarlet and the SSB aura inside being bright turquoise in hue.
Power and Usage
With this technique Goku retains all of the previous abilities of Super Saiyan Blue. Additionally, his substantial power gets further amplified by the linear boost in stats Kaio-ken has to offer. Hypothetically Kaio-ken is also capable of being added onto other forms such as Super Saiyan. However doing that will have no benefit as it'll kill the person immediately afterward. What makes Super Saiyan Blue Kaio-ken able to be executed as opposed to other Super Saiyan forms is that SSB is "a combination of strength and a calm mind, with proper ki control", thus the lack of control SSJ has would make it unsuitable to be integrated with Kaio-ken.
If one wanted to raise the power of this form even further, they could instead replace the regular Kaio-ken with higher levels such as Kaio-ken x 2, Kaio-ken x 3, etc. to mix in with SSB. With training, Goku has taken this combination to far greater heights, resulting in Super Saiyan Blue Kaio-ken x 10 and x 20. SSB Kaio-ken x10 originally caused the user's hair to dilate into a light cyan to somewhat whitish colorm with the rest of the body and clothing becoming deep red. However, as we see Goku use Kaio-ken x20 with SSB in the Tournament of Power Arc, he remains a normal color, with the exception of slightly red skin. After utilizing these forms Son Goku was able to fight back against Hit during his time freeze; a testament to its power.
Despite being the strongest form currently in the Saiyan's arsenal, it has also proven to have its considerable shortcomings. For one, due to the lack of mastery in this form, Goku only has a 10% chance of actually achieving it and a 90% chance of getting killed in the process. He also faced a severe inability to use his ki properly in the few days after the fight, virtue of the massive strain the form takes on him. Infirmities such as not being able to fly, lack of strength control and difficulty to focus with Instant Transmission were some conditions Goku had afterwards. Fortunately the affects were not permanent and Goku was able to make a full recovery. It is unknown if Goku combining SSB with Kaio-ken is still a gamble on his life or not.