For those who do not know how TSS works, you still can elect your preferred insurance company (Humano, Palic, Constitucion, whichever) and you contribute to TSS pool, TSS then gives its share of money to each insurance company based on the number of insured people. This is called Plan Basico de Salud. Some smaller insurance company offer no-fee increased coverage (e.g. you can wider coverage that PBS) at no cost. Most insurance companies offer supplemental insurance plans which you pay directly to them (not to TSS) and that way you can even-up to best private insurance plans. For example, ARS Constitucion has a 100-pesos-per-person supplement which evens up your PBS to their Tier-2 plan, and 200-per-person-per-month supplement evens up your PBS to their Tier-1 plan (very very good), and there are some more expensive supplements that offer you excess coverage that even NO PRIVATE insurance plans offers.
Advantages of PBS (and supplements) is NO EXCLUSIONS on pre-existing conditions, catastrophic illness, pregnancy, and NO WAITING periods. With a private insurance plan, you have to wait a month to visit emergency and lab tests, 2 months for a doctor's visit, 3 months for some more advanced testing, 6 months for outpatient surgery and even 12 months for non-emergency (they call it elective*) surgery. With PBS you have NO WAITING period, for anything. You're in today, and tomorrow you can go have an open-heart surgery.
* I don't know why they call it elective surgery, like anybody really "elects" to have open heart (or similar) surgery ... like ooh I feel like going for a 12-hour surgery this week, why don't you cut my chest in two so I can have a nice week-long hospital vacation...?