Maximum health can be increased with the implant type Vital Boost.
Maximum health can also be increased with the "Codename" weapons from the free DLC "Fire & Ice Weapon Pack".
How to determine how many health is needed ? To answer that question, we need to look at different aspect of the game.
First : as you may have noticed, ennemies deal a lot of damage. It is made that way to balance the mostly 1vs1 fights of the game. So most ennemies can kill you in few hits. None of them should be able to kill you in one or two hit if your gears aren't unupgraded. But if you need to always be at ~80% health, you will waste healing injectables by overhealing. Which lead us to the second aspect to look at, the amount of health restored by the different healing source.
But before that, let's take a look at the different source of healing and why it is important to not focus on just one (for most build).
Healing Source : for me, there is two different type of healing source. The main healing source, which are the Vital Injections. Here to save our skin if we make a big mistake or when we're at low health. And the "supportive healing source". They're here to mitigate the use of the main healing's source, Aggression Amplifier or Medi-Voltaic Injection are great exemple.
With that out of the way, we can go back to the original topic.
We know that we need enough health to survive few hits from the highly damaging ennemies of the game. We know that to not waste the main source of healing, we need to increase health even more. But raising your health to 400 with four Vital Boost (for exemple) ; when you're Vital Injection only restore 180, is a waste of implant slot. It will make you use more of the main healing source to get to full health or near it.
You could replace one Vital Boost for another option without impacting your survavibility.
The last aspect to look at is the defense. Which is mostly affected by your gears and it's upgrade level (mark). But at this point, you should just take a look at the Defense section.
With that knowledge, you should be able to judge by yourself how much health you need. If you need some exemple, you can try to look at different builds, in the Builds section (under reconstruction 13/07/2018).