In principle, could a brain be rewired to experience more pleasure and/or pain? I'm not sure if these are two separate questions, but I'm curious: in theory, could an existing adult mind/brain be modified to perceive pleasure/pain signals more intensely than otherwise? Without drastically changing the rest of the brain (i.e. while making sure that the brain is the same person; although this question is understandably complicated and potentially philosophical)?
As to the latter part of the question, the SCN9A gene might play a part. Maybe there exists a similar gene for pleasure?
(I made a post focusing on the genetic side on the biology SE. I think the questions are different enough for this to be acceptable, but it might be worth looking there to avoid duplicated effort.)
This is a difficult question to answer and likely can generate a variety of equally valid (or invalid) answers.
I thought to tackle this from a pathological vista - namely that of sensory processing sensitivity (SPS), which seemingly resembles your area of interest.
SPS can be defined as (Acevedo et al., 2018)

[A] genetically based trait associated with greater sensitivity and responsivity to environmental and social stimuli. [It] is characterized by greater empathy, awareness, responsivity and depth of processing to salient stimuli.

In their article the authors review the structural underpinnings as observed by fMRI scanning of SPS, alongside the brains of Autism Spectrum Disorder, Schizophrenia and Post-Traumatic Stress Disorder who also exhibit SPS alongside their other symptoms.
Common activated regions in all disease types were shown in the precentral gyrus.
SPS was associated with activity in reward processing centers (ventral tegmental area (VTA) and substantia nigra (SN), centers for regulation of bodily physiology and pain (hypothalamus and periaqueductal gray (PAG); self versus non-self recognition and empathy (inferior frontal gyrus (IFG) and insula), awareness and self reflection (temporoparietal junction (TPJ)) and self-control (prefrontal cortex (PFC)).
In terms of Autism Spectrum Disorder, Schizophrenia and Post-Traumatic Stress Disorder the authors continue with multiple brain regions that are activated commonly and uniquely with respect to SPS proper. I refer to the review referenced below for details.
I reckon, but am unsure, that re-wiring of the pathways or altering the structures themselves with, e.g., transcranial stimulation or with ablation techniques can emulate SPS symptoms, including pain and emotion processing. The practical ways to do this are difficult, given the complexity of the brain.
References
- Acevedo et al., Philos Trans R Soc Lond B Biol Sci (2018); 373(1744): 20170161