An Express Scripts spokesman said there was a difference between pharmacies like the one it owns that handle many drugs and “captive” ones that seem aimed at increasing sales of a particular manufacturer. Linden Care disputed that characterization, saying it was not owned by Horizon and dispensed drugs from other manufacturers as well.

The use of mail-order pharmacies for this purpose seems most common in dermatology, probably because many drugs for acne and other skin conditions are brand-name formulations of generic medicines. While the manufacturers argue that their particular formulations provide some extra value, health plans and pharmacy benefit managers do not always see it that way. They put high co-payments on these drugs to discourage their use, and pharmacies will often try to substitute generics.

So the drug companies have started to encourage doctors to submit their prescriptions to the mail-order pharmacies, which will not substitute a generic and which administer programs that subsidize the patient’s co-payments. The pharmacies also deal with the insurance companies, relieving doctors of the paperwork they would have to submit to justify their choice of an expensive drug.

Galderma, which is owned by Nestlé, sells the acne drug Differin, which costs at least $535 a tube, according to the website GoodRx.com. A tube of the generic form, adapalene gel, sells for about $100.

Galderma said in a statement that Irmat is only one of the pharmacies it uses and that most of its drugs go through retail pharmacies. It said it owned no pharmacies and no pharmacy handled its products exclusively.

Aqua is owned by the Spanish drug company Almirall, which said in a recent financial report that American dermatology sales grew 53.5 percent in the first nine months of this year. One of its big sellers is the acne drug Acticlate, which costs more than $700 for 30 tablets and is a form of the generically available antibiotic doxycycline. Aqua executives did not return calls seeking comment.

Irmat says in its complaint that Optum has known since 2013 that Irmat was mailing drugs out of state but didn’t take action until that operation grew to a meaningful size. Irmat’s revenue from Optum members increased from $2 million in 2012 to $15.3 million last year and a projected $33 million this year.