The way to break a monopoly is to provide another means. For healthcare, that means alternatives to company sponsored health plans, clinics, hospitals, doctors and nurses.
The answer is to decline a health plan altogether and go with the underground medical care (as opposed to the UMC). Foreign witch doctors and midwives, drug dealers dealing medical drugs instead of pleasure drugs, weird underground "clubs" with hidden curtains, passwords, bodyguards that actually dispense health care, and an active network of patients on the web that grants you access. Perhaps another establishment could be a front for the business. I suggest the church as a natural front. Whatever's a cliche in the seedy underground is fine. The way to avoid quacks is to network with each other, perhaps even real doctors will help. The police shouldn't bother if they go there too.
