Why doesn't the Byakugan have a second stage? The Uchiha Clan had the Sharingan which  has a lot  of different stages: 


Sharingan (Increases power with age/3 commas = maturity)
Mangekyo Sharingan (Unlock = Kill a close friend/family member) (Blindness over time)
Time Erase (Kasashi's Mangekyo Sharingan)
Eternal Mangekyo Sharingan (Perfect vision/Incredible Power)
Amaterasu (Invincible Fire Attack)
Tsukuyomi (Illusion Technique)
Mind Control (Shisui Uchiha 'Mental Genjustu')
Copying Ability (Endless library of techniques) (See opponents techniques/Mimic opponent)
Susano'o (Giant Skeleton/Invincible Sword 'Totsuka Blade'/Invincible Shield 'Yata Mirror')
The Blade and Mirror were found by Itachi, by unknown means - Teleportation
Intangibility (Madara Uchiha)
Izanagi (Dream/Illusion Technique)
Sharingan+Rinnegan Techniques
Mangekyo/Eternal Mangekyo 


And it varies for each user in shape and appearances:


Sasuke Uchiha - Six-Sided Star Shape (Mangekyo) Six-Sided Cyclone (Eternal)
Itachi Uchiha - Three-Sided Cyclone
Kakashi Hatake - Bizarre Three-Sided and Curved Cyclone
Madara Uchiha - Izuna Uchiha - Stange Opened Circle with Three Squarish-Openings
Shisui Uchiha - Four Sided Throwing Star


But the Byakugan stays the same and every member has the same one.

So it makes me curious, why doesn't Byakugan have a second stage?
There is a &quot;second stage&quot; of the Byakugan, called Tenseigan. And it has its own Chakra Mode, which is said to be on par with the Naruto's Nine-Tails Chakra Mode.
When the Byakugan is combined with the chakra of an Ōtsutsuki clan member, it evolves into the Tenseigan. The only known wielders are:

Hamura Ōtsutsuki
Toneri Ōtsutsuki


The Tenseigan has abilities similar to the Rinnegan.

The Tenseigan allows the user to control both attractive and repulsive forces, similar to the Rinnegan. Additionally, it also grants the wielder Tenseigan Chakra Mode, which in turn gives the user an increase in speed, power, strength, durability, and reflexes. It also grants its user Truth-Seeking Balls, thus granting the user all five nature transformations and Yin–Yang Release.
source: Naruto Wikia