The Scribing system, which allows players to unlock new skills which can be customized, should also be introduced for the Companions system to allow players to create the perfect skills for their Companions. First, I'll recap what we already know about the Scribing system, then I'll discuss what features of the Companions system can be tweaked, and emphasize how adding Grimoires to the Companions system would benefit it.
The Scribing system allows us to customize the primary, secondary, and tertiary effect of a Grimoire skill, which is tied to some existing skill line. The base effect of the skill cannot be changed, but we can change things like the damage type, the resource cost, which effect is triggered when the skill is used, and so on.

So, what of the Companions combat system? Well, there are many skills which have a cost in either Ultimate or a cooldown, and some of those skills by default will target just the Companion themselves (such as Snow Squall), just allies (such as Reverse Entropy), just enemies (such as damaging abilities), or the Companion as well as allies (such as Rejuvenation). Additionally, some of those skills have more proc conditions which determine when to cast the skill based on a Health threshold, whether the target is nearby, whether the target is taunted, and so on:

The Scribing system would be a brilliant way to add new Companion skills which can have their proc condition and target tweaked. There are many facets to the Companions combat system, such as how to determine the cooldown for each ability and how much damage or healing they do, but there are also many parallels to what we know of the Scribing system, such as the cost of abilities being determined by which modifications are made to the Grimoire.
For instance, a Companion's Grimoire skill given the "Used when the enemy is below 25% Health" condition could be given the Companion's execute levels of damage as well as the 8 second cooldown. A player could choose whether to make a healing Companion Grimoire target just the Companion, just players, or both, which can help when building a Companion to focus on keeping either themselves or their allies alive. Modifying the cast condition and the targets affected would affect variables such as the skill's cooldown, the damage/healing done, and so on.
Alternatively, maybe the players would instead choose Grimoire effects such as "Execute", "Taunt", or "Restoration over Time", which would then cause the relevant proc condition ("Used when the enemy is below 25% Health", "Used when the enemy is not already taunted", "Used when Companion or an ally is below 75% Health") to be applied to the Companion Grimoire skill. It's possible to stack proc conditions (such as Isobel's skill Holy Ground, which can proc given a Health threshold or an enemy's proximity), so it seems reasonable that a Companion Grimoire should allow for very versatile skills to be made for our Companions.
In summary, the Scribing system should allow for customizable Companion skills which can utilize the existing Companion skill proc condition system to allow players to customize how their Companions perform, which can be relevant in content such as the Infinite Archive and in the overworld. Is there any chance that there has already been some talk about how the Scribing system could be used with the Companions system?
@ZOS_PhilipDraven @ZOS_Kevin
PC/NA — Lone Werewolf, the EP Templar Werewolf
Werewolf Should be Allowed to Sneak
Please give us Werewolf
Skill Styles (for customizing our fur color),
Grimoires/Scribing skills (to fill in the holes in our builds), and
Companions (to transform with).