You can count the number of stocks that trade on U.S. exchanges and have a market cap of $1 trillion or more on one hand -- and you won't have any fingers left over.

However, there are several stocks that are theoretically within striking distance of reaching that level. Some of them might easily come to mind, such as Tesla. But here's one stock that could join Apple and Amazon in the $1 trillion club that you might have overlooked.

Not an AI stock

Artificial intelligence (AI) serves as a common catalyst for the five stocks that have already hit $1 trillion market caps. However, AI isn't the major driver (at least, not at this point) for big pharmaceutical company Eli Lilly & Co. (LLY -1.95%).

Just three years ago, the thought of Lilly reaching a market cap with 12 zeros in it would have seemed far-fetched. But the pharma stock has skyrocketed more than 275% since then, including an impressive 50%-plus gain so far in 2023.

Today, Lilly's market cap is over $525 billion. The company ranks as the largest drugmaker in the world by far. Lilly's tremendous recent success is due primarily to four drugs: Jardiance, Mounjaro, Taltz, and Verzenio.

Jardiance and Mounjaro are helping Lilly extend its leadership in treating diabetes. Taltz enabled the company to carve out a place for itself in treating autoimmune diseases, including plaque psoriasis and psoriatic arthritis. Verzenio positioned Lilly to remain a top player in the cancer arena.

How Lilly could reach $1 trillion

To reach $1 trillion, Lilly needs its stock to climb another 90% or so. Is that goal a realistic one? It's possible.

Mounjaro stands out as a critical component of Lilly's future. The drug is currently approved for treating type 2 diabetes. Lilly expects to win U.S. approval in treating obesity as early as late 2023. 

BMO Capital analyst Evan Seigerman estimates that Mounjaro could generate peak annual sales of close to $69 billion if approved for weight loss. That projection is admittedly higher than others. Still, Wall Street's consensus is that Mounjaro's sales could top $50 billion per year. That would put it on course to potentially become the best-selling drug in history.

But Mounjaro isn't the only game-changing medication for Lilly. The company also hopes to secure U.S. approval for Alzheimer's disease therapy donanemab by year-end. Morningstar projects that the drug could achieve peak annual sales of more than $7 billion. 

Jaypirca is another potential blockbuster of the future. It has already won U.S. approval in treating mantle cell lymphoma and awaits a decision in treating chronic lymphocytic leukemia. 

Lilly's pipeline features several additional promising candidates. They include Crohn's disease drug mirikizumab, obesity drugs orforlipron and retatrutide, and Alzheimer's disease drug remternetug. 

Meanwhile, the aforementioned Jardiance, Taltz, and Verzenio continue to deliver double-digit percentage sales growth. Lilly also has several other products with exceptional momentum, notably including cancer drugs Cyramza, Retevmo, and Tyvyt. 

What could get in the way

Lilly isn't a shoo-in to join the $1 trillion club in the next few years. Drugmakers always face the possibility of clinical trial flops and regulatory rejections. Even if Lilly overcomes these hurdles, its products might not achieve the commercial success that analysts predict.

It's also likely that other companies could join Apple and Amazon before Lilly does. Tesla, Warren Buffett's Berkshire Hathaway, and Facebook parent Meta Platforms have larger market caps.

However, Lilly appears to be the odds-on favorite to become the first healthcare stock to reach a $1 trillion market cap. It could take several years to get there, though.