Nearly every giant company started out as a much smaller one. Investors who got in early were able to realize huge returns. So which smaller companies have the potential to grow much larger today?

Three Fool.com contributors have ideas on up-and-coming growth stocks to buy right now. Here's why they chose Axsome Therapeutics (AXSM 0.76%), Sarepta Therapeutics (SRPT 1.06%), and Travere Therapeutics (TVTX -3.12%).

Not a one-trick pony

Keith Speights (Axsome Therapeutics): Some small drugmakers have all of their eggs in one basket with only one pipeline candidate. But Axsome Therapeutics definitely isn't a one-trick pony: The company already has two drugs on the market and could add two others in the near future.

Axsome didn't develop sleep-disorder drug Sunosi; it bought the rights to the drug from Jazz Pharmaceuticals and relaunched it. The company has already seen solid U.S. sales growth for Sunosi. International sales could pick up as well, with a recent deal licensing commercialization rights in Europe and parts of the Middle East and North Africa to Pharmanovia.

Auvelity (also known as AXS-05), on the other hand, was and is Axsome's baby. The company launched Auvelity in October 2022 as a treatment for major depressive disorder. Axsome is also evaluating the drug in treating Alzheimer's disease agitation and smoking cessation.

The two other drugs that could be on the way to commercialization are AXS-07 and AXS-14. Axsome plans to refile for U.S. Food and Drug Administration (FDA) approval of AXS-07 in treating migraines in the second half of 2023. It also expects to submit for FDA approval of AXS-14 in treating fibromyalgia this year.

In addition to these products, Axsome's pipeline features two other clinical-stage programs. The company is evaluating AXS-12 in a late-stage study targeting narcolepsy. It also plans to advance solriamfetol into phase 3 testing as a treatment for attention deficit hyperactivity disorder (ADHD) within the next few months.

Unlike some biotechs, Axsome doesn't have to worry about raising capital. CFO Nick Pizzie said in the fourth-quarter conference call that the company's current cash and term loan facility should fund operations until it's generating positive cash flow.

Axsome's market capitalization stands at around $2.8 billion. With Auvelity and Sunosi plus other drugs likely on the way to market, I predict that this stock will deliver strong gains over the next few years.

This biotech is slowly making a name for itself 

Prosper Junior Bakiny (Sarepta Therapeutics): Sarepta Therapeutics is a biotech company that certainly isn't one of the household names in the industry. But that's no reason to ignore this genetic medicines specialist.

Last year, Sarepta's revenue jumped by 33% year over year to $933 million. The company owes this performance to its portfolio of medicines that treat Duchenne muscular dystrophy (DMD), a rare genetic disease that leads to muscle degradation.

All three of Sarepta Therapeutics' approved medicines target DMD, a condition with few treatment options. And what's more, the biotech is seeking to expand its lineup. Last year, the company sent an application to regulatory authorities in the U.S. for SRP-9001, a potential new DMD medicine it developed in collaboration with Roche. The U.S. FDA set a PDUFA goal date (by which it should complete the review of Sarepta's application) of May 29.

Sarepta estimates potential peak annual sales of $4 billion for SRP-9001. And the company shouldn't stop there. It still has several potential DMD treatments in the works. In addition, Sarepta has over 40 pipeline programs, not just those targeting DMD.

The company focuses on rare diseases. One of the advantages of this strategy is that there are often very few (if any) approved therapies for rare illnesses, so launching one can allow drugmakers to dominate the market with few competitors.

Sarepta Therapeutics has already proven the potential of its genetic medicines platforms, and investors can expect more approvals in the years to come. That's how Sarepta Therapeutics could rise in prominence and become a well-known, well-established biotech stock. 

A recent FDA approval makes this stock attractive

David Jagielski (Travere Therapeutics):  One stock that healthcare investors should have their eyes on right now is Travere Therapeutics. At a market cap of around $1.4 billion, this is a modestly sized business that could get a lot bigger. 

Last month, the U.S. FDA granted accelerated approval for Filspari, the company's drug to treat chronic kidney disease. At a list price that could be as high as $100,000 per year, this is a high-priced drug that could generate significant revenue for Travere in the future.

At its peak, for the U.S. market alone, it could hit $745 million in sales. That's not bad for a company that generated just $212 million in revenue last year, which came primarily from the sale of bile acid and tiopronin products.

At only $21 a share, this is a stock that has significant potential. The consensus analyst price target is at just under $33, which suggests an upside of more than 55% from where it's trading right now.

There is, however, some risk with the stock. Travere isn't profitable, and in the past year it has burned through $186 million in cash over the course of its day-to-day operations. But with more than $450 million in cash and short-term investments on its books as of the end of last year, it isn't about to run out of money anytime soon.

If you're patient and willing to stomach some risk, this could be a growth stock that leads to great returns in the future. The stock's low valuation and recent drug approval could also make Travere an attractive acquisition target for a larger healthcare company.