Try BCAA or Westland Insurance for supplemental coverage.
To confirm what you already know:
https://www.preszlerlawbc.com/services/icbc-claims/what-is-the-difference-between-icbc-and-private-insurance/
ICBC insurance
There is one obvious reason ICBC insurance coverage is so prevalent:
obtaining a policy is mandatory. Any British Columbia driver that wishes to register or drive a vehicle must first obtain an ICBC insurance plan. This basic coverage requirement covers the bare minimum level of insurance.
The basic plan every driver must purchase covers up to $200,000 in bodily injury
and property damage for third-party liability. This policy covers claims from third parties based on your negligence. These basic plans also provide under-insured motorist protection for medical expenses caused by under-insured drivers.
Speaking of medical coverage, the basic policy also provides up to $150,000 of medical coverage per person. Following a hit and run accident, ICBC also provides up to $200,000 in coverage.
ICBC policies are always the primary policy. Because they are mandatory, these policies will provide the initial source of compensation after a crash. That said, it is possible to have private insurance policies that supplement your ICBC coverage.