That opens the door for patients abusing their own medication, or the pills being abused by relatives or friends of a patient.
To reach its reduction goal, Intermountain will be using a "data-driven approach" spearheaded by a "business intelligence tool" that the health-care system developed to track prescriptions and develop guidelines for appropriate prescribing practices, Harrison said.
Intermountain also already has trained about 2,500 of its caregivers as part of the opioid reduction initiative.
Sales of prescription opioids have quadrupled since 1999, despite the fact that "there has not been an overall change in the amount of pain Americans report," according to the federal Centers for Disease Control and Prevention.
Utah, where most of Intermountain's facilities are located, has been particularly hard hit by the opioid crisis, with the state being ranked anywhere from seventh to 12th in the nation for overdoses, Harrison noted.
Intermountain, which has 850,000 members in the health insurance plan it operates, each year has some kind of interaction with 1.2 million people in Utah, which has a population of just 3 million.
"This is a big goal," Harrison said of the 40 percent reduction target.
"But our communities and the people in them are suffering, and we need to do something about that."
Harrison said that the prescription practices at Intermountain, which prescribes about 12.5 million opioid pills to patients with acute pain annually, have been "no better, no worse" than other health-care systems.
But "we can see that there's enormous variation" in the amount of painkillers being prescribed by different doctors across Intermountain's system, Harrison said.
"What you're seeing is what happens when there are not a lot of guidelines" about what an appropriate amount of pills are to be prescribed for various health situations, Harrison said.
Given this variation and analysis of prescribing patterns by Intermountain's staff, "they actually think that 40 percent [reduction] is a really good place to start ... there actually may be more room to move," Harrison said.
The experience of Kaiser Permanente, a major health-care system based in California, suggests that Harrison may be correct.
In 2009, Kaiser Permanente's Southern California division began an effort to reduce the number of patients who were getting high doses of opioids.
That move was launched after a group of doctors in the system noticed that the opioid hydrocodone was the most prescribed medication in Kaiser Permanente's health management organization in Southern California, while another opioid, OxyContin, was also high on that list.
"People [were] getting prescriptions for a thousand pills," Dr. Steve Steinberg, a Kaiser physician, told Atlantic.com for a story about Kaiser's program published in March.
"The numbers were so striking that it led us to look into it," Steinberg told the news site.
Kaiser Permanente has since expanded its opioid prescription initiative to its operations nationally.
According to data from Kaiser's Dr. Sameer Awsare that was provided to CNBC, Kaiser Permanente's system nationally reduced opioid prescriptions by 40 percent from December 2014 to this past February.
Awsare also said that it has decreased prescription amounts of OxyContin by 75 percent. The health system noted that OxyContin has a high potential for diversion and abuse because brand-name opioids have a higher street value.