Emotional Intensity (BPD) is caused by early life relational disruptions that result in the development of fragmented self-states (what Otto Kernberg calls primitive dissociation or "splitting"), these states are easily triggered and come with overwhelming emotions and impulsivity. Also there are problems with focus, attention and a shifting sense of self and identity. Affect Regulation Theory sees a self-state as a combination of the emotion-regulating system and a set of "discrete coordinated" cognitive, attentional, perceptual, representational, memory, and reflective systems. [4, 9]
Brain research has shown that fragmented selves require a mindfulness/witnessing stabilization phase where you notice the instability dampen down and a more stable sense of self emerge  and a c-PTSD intervention phase to transform any implicit maladaptive emotional schemes, Janina Fisher calls this developing a "Witnessing Adult Self" that holds her younger emotional inner child parts and the more fragmented we are the more we blend with our younger child parts. The more we are able to get our protective parts to relax and be with these emotional parts the more our affective neural systems will stabilize and transform into a core calm state. [2, 5]
The stabilization phase relies a lot on coping skills (like DBT, Mindfulness, Mind Training, Meditation, Yoga, Neurofeedback, Tai Chi, Art Therapy, Distraction, Support Groups) and focused attention and awareness training combined with (self-)compassion. Also developing and internalizing safe spaces and objects of support (friends, family, therapist, animals, spiritual figure) is crucial in healing the emotion regulation brain networks. [8, 9, 10, 11, 12]
Dr. Marsha Linehan - Becoming One:
Neuroscience has shown that strengthening the prefrontal brain areas inhibit emotional reactivity and instability, 75% of the amygdala is dedicated to detecting danger, with emotional instability / complex trauma there is often an abnormal amygdala and it's weakened prefrontal connections. Through stabilization you are able to create space between your Self and your emotional parts and can start to integrate these disowned younger traumatized parts through acceptance and compassion. [3, 6, 8]
Emotional Intensity (BPD) is characterized by what in the literature is called affect dysregulation, because of an hyperactive emotional center in the brain (amygdala) and underdeveloped inhibition (right orbitofrontal cortex), people with this disorder experience intense emotions that are easily triggered, they also trigger into states of numbness/detachment (dissociation/depersonalization) and emptiness. [see Chronic Emptiness]
The combination of these symptoms are very distinctive for Emotional Intensity / Borderline and are caused by early attachment/developmental trauma. It is considered a Complex Trauma Disorder by experts and required to be treated as such. 
Infants co-regulate through their caregiver, this is because we fully depend on them when we are born and have cues like our cry for help.
To make sure we get our needs met humans have an attachment system. When our caregivers are predictable and consistent we develop a secure sense of self to discover the world, but when our caregivers are not consistent, predictable or even fearful themselves our attachment system can become dysregulated and hyperdependent and we rely on others to regulate our emotional states.
These issues often come co-morbid with a life filled with traumatizing experiences also known as Complex Trauma (c-PTSD). These experiences and ways of coping like SH/ED/Addiction can result in lots of different diagnosis and labels like ADHD, PTSD, MDD, DD, Bipolar even a misdiagnosis of Autism.
The beginning of stabilizing this system of intense affect/emotion is Awareness, Focused Attention and Compassion for self and other and developing new resources (Sensorimotor) and safe spaces (support network, therapist, animals, spiritual figure). This strengthens the areas that inhibit our emotional systems and longer term shrinks them (like the right amygdala). Because of phobias for emotions, for some people this work has to be done with another person or therapist to act as a source for co-regulation, it is important to internalize the positive feelings such therapeutic alliances provoke and explicitly metacognitively process them. Also these days tools like brain wave measurement devices (like in Neurofeedback) are used to aid the process of learning to regulate bodily states (Bessel van der Kolk, 2021).
This is what Dan Siegel calls Three Pillar Mind Training and what DBT (an evidence-based treatment for emotion disorders) calls Mindfulness. Dan Siegel has a Wheel of Awareness practice where you go through all the senses and our 6th and 7th our body and mental activities and our 8th, the interconnection with the larger whole. This practice integrates our brain area's responsible for conscious awareness, social attunement and emotion regulation. These three elements integrate in the same frontal brain area's.
Barry Boyce on mindful.org: "The fear that our emotions will overtake us and rule our lives (or at least a significant chunk of our time) is indeed one of the reasons we seek mindless distraction. Being kind to ourselves, repeatedly, is job one. Mindfulness practice is not about aggressively “tackling” our emotions in a fight to the death. If we’ve been suppressing something for a long time and mindfulness begins to bring it up into our conscious awareness—as it will—the key instruction is to notice it and move on. When it comes up again, maybe seconds later, we do the same. This approach of a little bit at a time, moment by moment, reduces the emotional wallop by breaking it into momentary pieces, rather than treating it as one big permanent thing, which it is not."
Other different ways of Mindfulness training are brain wave / classical / instrumental music, meditation, yoga, tai chi, body movements, creative arts, relaxation, active social engagement.
The reason this is important is because Mindfulness practices activate the vmPFC (frontal lobe) area of the brain and strengthens emotional inhibition, another important component is training Cognitive function like memory, planning, goal setting but also journaling, autobiographical authoring and self-reflection. Emotion dysregulation is caused by lack of integration between brain areas that come together in the prefrontal cortex, the area responsible for self-reflection, attention but also social attunement.
Another distinctive symptom in people with Emotional Intensity is a state of feeling empty, this feeling relates to early attachment experiences that resulted into feeling a lack of self. It is hypothesized as being on the lower spectrum of dissociation where you are disconnected from your emotions but also from the right brain area's of Self.
Understanding chronic feelings of emptiness in borderline personality disorder: a qualitative study
Caitlin E. Miller, Michelle L. Townsend & Brin F. S. Grenyer
Borderline Personality Disorder and Emotion Dysregulation volume 8, Article number: 24 (2021)
Chronic feelings of emptiness were experienced as a feeling of disconnection from both self and others, and a sense of numbness and nothingness which was frequent and reduced functional capacity. Feelings of purposelessness and unfulfillment were closely associated with emptiness, and most participants experienced emptiness as distressing. Responses to feelings of emptiness varied, with participants largely engaging in either impulsive strategies to tolerate feelings of emptiness or distracting by using adaptive behaviours. Most participants distinguished chronic feelings of emptiness from loneliness, hopelessness, dissociation, and depression.
When things become so overwhelming your body has a protective numb/detached state called dissociation (depersonalization/derelation form), in this state you or the world around you feels unreal and you can feel like you're outside of your body watching yourself. This state can also be confused with treatment-resistant depression, also Bipolar depressive episodes are dissociative. Medications can make these symptoms worse. Mindfulness and grounding practices are ways to get out of these states but another recommended way is the practice of IFS/Parts Work.
Protective parts like dissociation or managers that try to control us should be befriended by exploring their fears and asked to step back or wait in a room, they are trying to prevent wounds from being triggered, IFS is a evidence-based complex trauma model designed for people with fragmented Selves (Bessel van der Kolk, Richard Schwartz, Janina Fisher, Daniel Siegel, Allan Schore, Frank Anderson, Arielle Schwartz, Russell Meares, Markus West, 2021).
It is possible to experience stress transient symtoms of paranoia or hallucinations like voices. These symptoms are seen in different kind of trauma survivors including war veterans. These symptoms are your internalized trauma protections "split off" to the outside and should not be feared but befriended, often the voices represent an internalized critic.
Medications can make these symptoms worse too because they are dissociative. These are your protective parts stuck in a past traumatizing time where they were needed for survivial, they have good intentions but are stuck in their fears and are trying to manage your life. Stabilization combined with c-PTSD Parts Work is the best way to integrate your neural systems and remit these symptoms.