Next Form is the form that the CPUs (Purple Heart, Black Heart, White Heart and Green Heart) take after utilizing the power of the Hyper Share Crystal. It is an evolution past their normal goddess forms.
The new, Next-Gen form the four CPUs awoke to using the Hyper Share Crystal. It is more powerful than any HDD state that came before it. Not only do the weapons of the goddesses upgrade specifically for Next Form use, but their Processor Units have various attack gimmicks incorporated into them, too.
Additionally when in Next Form, the goddesses undergo yet another personality change -- becoming notably calmer than their previous states. Their voices also become noticeably lower.
The goddesses gain new divine names exclusively for this form. The word "Next" is added in front of their names and "Heart" is dropped completely. For example, "Purple Heart" changes to "Next Purple".
In terms of gameplay, the Next Form doesn't increase stats, rather it keeps the stats from HDD, increases the strength of all skills, decreases skill costs, increases the size of circular area of effect skills (skills that hit in a line keep the same range), and gives access to an exclusive, powerful attack. It counts as a transformation above HDD, as such, Coupling and Formation Skills will only work with other Next Form CPUs. Instead of using the SP bar, it will consume 1 EXE level to activate the Next Form.
Since it is a transformation it will activate the appropriate effects from passives and game discs. However, despite being technically a second transformation, T. Performance, which lowers skill costs after transforming, will not activate a second time, just readjust itself in accordance to the new skill costs.
T. Performance will always take 10% off of the skill, meaning it is less noticeable in Next Form due to the already reduced costs. The cost reduction of each skill depends on whether it is single target or area of effect. Single target skills are reduced by 60% while AoEs are reduced by 50%.