Fifteen years gives a strong business plenty of time to become something much larger.
That is the sort of opportunity I would be looking for. I want companies that are already proving themselves today but still have several ways to grow from here.
These are three ASX shares I would be happy to buy with that timeframe in mind.

Image source: Getty Images
Pro Medicus Ltd (ASX: PME)
Pro Medicus has already become an important provider of medical imaging software to major healthcare systems, particularly in the US.
But despite winning some very large customers, the company estimates it still has only around 11% of the US market.
I think that leaves a substantial opportunity ahead.
Visage has already shown that it can handle the demands of large hospital networks, so Pro Medicus can keep taking that proven technology to more healthcare organisations over the years ahead.
There is also room to do more within existing customers. The company is expanding beyond radiology into cardiology and enterprise imaging, which could allow Visage to handle a greater share of the medical images produced across a healthcare system.
Medical imaging volumes should also keep rising as populations age and healthcare becomes more reliant on scans. Artificial intelligence could make the platform even more valuable as hospitals look for better ways to analyse those images and manage growing workloads.
With so much of the US market still available, I think Pro Medicus has plenty of room to keep growing for years.
Hub24 Ltd (ASX: HUB)
Hub24 has built an important position in Australia's wealth management industry.
Its investment platform helps financial advisers manage client portfolios and superannuation, putting the company behind a growing amount of Australian household wealth.
Hub24 has been expanding the technology available to advisers through businesses such as Class and myprosperity. That gives it more ways to help advice practices with administration, reporting, client engagement, and other everyday tasks.
The more of that work Hub24 can handle, the more important its technology can become to advisers.
Australia's superannuation system provides another long-term tailwind. Workers keep contributing throughout their careers, while investment returns can increase the value of existing savings.
Hub24 therefore has the chance to win a larger share of a market that itself should continue growing.
If it keeps improving its technology and strengthening adviser relationships, I think the business could look considerably larger by the early 2040s.
Life360 Inc. (ASX: 360)
Life360 is an ASX share that has built a service that millions of families use as part of everyday life.
Location sharing remains at the centre of the platform, but I think the longer-term opportunity comes from how many other family safety needs can be addressed around that relationship.
The company has already expanded into driving safety, emergency assistance, identity protection, connected devices, pets, and services aimed at ageing family members.
Growing the number of paid subscribers remains an important part of the story, including converting more free users over time. But I see that as one part of a wider opportunity to make Life360 more valuable to each household.
International growth could also become increasingly important.
Life360 already has users across a huge number of countries, giving it the chance to build stronger businesses outside the US as awareness and adoption increase.
If the company keeps finding practical ways to help families protect the people and things they care about, I think it could become a much more substantial consumer technology platform over the next 15 years.
Foolish takeaway
A 15-year investment does not need every year to go smoothly.
What I want is enough time for strong businesses to develop new products, enter larger markets, deepen customer relationships, and keep building on what they have already achieved.
I think Pro Medicus, Hub24, and Life360 all have that sort of runway.
That is why I would be comfortable buying all three today and giving their long-term opportunities plenty of time to develop.