I gather they call it 'doctor shopping.'

That was what Limbaugh got hit with a few years back:

http://www.drug-addiction.com/doctor_shopping.htm

According to the Drug Enforcement Administration (DEA), "doctor shopping" is one of the primary ways that addicts obtain prescription drugs for non-medical use. "Doctor shopping" refers to when an individual visits several different doctors to obtain prescriptions for the same medications, and then has the prescriptions filled at different pharmacies. his allows the individual to obtain more of the prescribed substance than any one physician or pharmacist would allow. Legally, doctor shopping is not a minor matter; it is prosecuted as a felony and is punishable by up to five years in prison.

In 2006, one of the most famous doctor shopping and prescription drug abuse stories came to light. Conservative talk show host Rush Limbaugh turned himself in to Palm Beach authorities for doctor shopping. From 1998 to 2006, Limbaugh obtained massive amounts of the painkiller OxyContin, both through multiple prescriptions from different health care providers and through illegal channels. Limbaugh began taking painkillers in the late 1990s after an unsuccessful back surgery. By the time he turned himself in to police, he was rumored to be taking up to 30 pills per day. His drug abuse was severe enough to damage his hearing.

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