SAN FRANCISCO — Apple Inc. has some more high-profile fashion and luxury brands in its corner in its patent infringement case against rival Samsung Electronics Co. Inc.

Late Friday, academics, designers and brands piled on in Apple’s ongoing legal battle against Samsung. Fashion brands such as Tiffany & Co., Adidas AG, Crocs and Jenny Yoo, in addition to organizations such as the American Intellectual Property Law Association, submitted briefs to the Supreme Court in support of Apple’s case.

Those briefs come a day after an amicus filing on Thursday that contained 111 signatures, including designers such as Calvin Klein, Alexander Wang, Nicolas Ghesquière, Dries Van Noten, Alber Elbaz, Sir Paul Smith and Chitose Abe of Sacai, in addition to others representing various design fields.

An amicus brief is a document filed by a “friend of the court,” meaning that the parties are not directly involved in the case; but the non-parties generally have something to gain (or lose), depending on the verdict. The Apple vs. Samsung case has implications for a wide range of design fields, including fashion and industrial design, and potential punishment if a company infringes on a design patent.

The briefs stem from a lawsuit that Apple filed against Samsung in 2011, charging the South Korean electronics company with infringing on its patents and directly copying the design elements and technologies of its iPhone. A lower court in the U.S. ruled in Apple’s favor, but now it’s up to the Supreme Court to determine precisely how much of Samsung’s profits should be paid to Apple to compensate for the infringement. Samsung is challenging whether it is liable for $399 million out of a total of $548 million it has paid to Apple so far. Since 2011, Apple and Samsung have been involved in as many as 50 lawsuits in 10 countries. Samsung has won rulings in South Korea, Japan and the United Kingdom.

Samsung said that the $399 million was awarded to Apple based on infringement of three patents in question — a black rectangular round-cornered front face, a bezel and a colorful grid of 16 icons. Those patents, Samsung alleged, cover only “specific, limited portions of a smartphone’s design.”

Under discussion in the case is section 289 of Title 35 of the United States Code, which states when a design patent is infringed upon, the offending party must pay the owner the full profit made from sales of the offending design. The federal circuit court, Samsung asserted, held that Apple is entitled to the entire profits of the copied phone sales “no matter how little the patented design features contributed to the value of Samsung’s phones.”

“In other words, even if the patented features contributed 1 percent of the value of Samsung’s phones, Apple gets 100 percent of Samsung’s profits,” the South Korean company said in its appeal. The High Court agreed to consider the legal question of whether total profits from the sale of an infringed product should be awarded to a company if the design patent applies only to the component part of a product.

And this is where the fashion world has a horse in the race.

Thursday’s brief, whose lead representative was Charles Mauro, founder and president of Mauro New Media, stated: “When an infringer steals the design of a successful product, it captures the consumer’s understanding of what the product does and what the product means in addition to the emotional connection associated with the company’s brand.”

The current statute requiring total disgorgement of profits from the sale of an infringing product, “remains sound and perfectly aligned with modern cognitive science,” the designers argued in the Thursday brief. “Indeed, disgorgement of total profits is the only appropriate remedy for design patent infringement.”

In the Friday brief, Tiffany, Adidas and Jenny Yoo Collection made an impassioned argument for why the High Court’s decision is relevant to the world of fashion, and emphasized the economic impact on the industry. The companies said they “have an interest in highlighting the unique function of design patents in the fashion industry, which differs in various ways from the technology industry.” The brief said that the Supreme Court’s decision would directly affect the value of their design patents and the designs that those patents protect.

They called out design pirates who capitalize on huge investments made by fashion designers, and argued that the total profits element of section 289 “is critical to address the harm caused by design piracy. The total profits rule helps to ensure that designers have the appropriate incentives and rewards to make investments in innovative designs.”

Crocs, in a separate brief filed Friday evening, made an argument for implications “outside of the smartphone context,” and said that its designs are “almost one and the same” with the brand.

“Simply put, for companies in industries such as footwear, apparel, accessories and appliances…design can be paramount — a chief differentiator in the market, a driver of sales and the lifeblood of the business.” Crocs said that “requiring a showing of apportionment” — in other words, Samsung’s argument against paying the total profits — “would severely harm Crocs’ ability to create, protect and share its innovative designs.”

Mauro said in an interview that the implications of the case for all designers are “very direct.”

“At the heart of the case of what Samsung is actually proposing is a complete rework of how infringers have to compensate parties that they’ve infringed with respect to design patents,” he said. “Currently, if I infringe on your design, and I am found legally to have done so then I must [compensate you] all of the profits gained from the sale of my product that infringes on your product. That’s called a disgorgement of total profits.”

In seeking the 111 signatures in the Thursday brief, Mauro’s firm contacted a list of people in each field, many of whom came from his network, he said. To help them understand the potential implications of the case, the firm created a web site, at http://designpatentprotections.squarespace.com/. To date, no large legal industry group has filed in support of Samsung.

Mauro said the law has been in place since 1887. This is the first Supreme Court design patent case in more than 100 years; the oral arguments will begin on October 11.

“By Samsung asking the court to change the way infringers are asked to compensate those that are infringed, they will basically have dramatically reduced the impact of design patents and they will also dramatically increase the complexity of design patent litigation,” he claimed.

“The compensation method goes from something that is extremely simple – probably the most simple compensation model ever written by the U.S. Congress, that being I have to give you all of my profits – to now something that requires a large team of experts on both sides. There will be arguing over which features have value, how much the features have and we see it as essentially an existential threat to design and design expertise across all fields,” Mauro said.

It would essentially remove the major disincentive—full disgorgement of profits – to copy products designs, Mauro claimed.

“We would expect to see within a few years a massive influx of copycat products in the U.S. and we will certainly see a diminishing impact of design,” he added.

Rachel Wainer Apter, an attorney with Orrick, Herrington & Sutcliffe, LLP, which crafted the first brief representing the designers, used a Volkswagen Beetle as an analogy.

“In the case of Volkswagen, there [is currently] no incentive to completely copy the Beetle because you know you have to disgorge any of the profits that you made from the sale of your copycat car,” she said. “But if going forward you don’t have to disgorge all profits made from the sales of your copycat cars [and] instead you can keep the profits that you can show are due to the engine, due to the carburetor and due to the wheels and you are only having to disgorge the small amount of profit you are claiming from the shell, then there will be a huge incentive to copy.”