The Food and Drug Administration on Monday proposed a new framework for enforcing health and safety rules against homeopathic medicines that could lead to warning letters, involuntary seizure or criminal investigations against some companies.

The agency is focusing on a variety of homeopathic products, including those that have already reported safety concerns or that are aimed at people who are vulnerable, including people with addictions or who have cancer or heart disease. This means the FDA will more aggressively go after certain manufacturers, but under the proposal, the vast majority of homeopathic remedies would remain on the market.