Yes, in most cases your portal can search a trip with several stops in one go, as long as the flight supplier behind it supports that kind of search. This is usually called a multi city search, and it lets your customer set a different city and a different date for each leg of the journey, instead of only choosing a going date and a coming back date.
How well it works depends on which supplier you are connected to. A full airline reservation system will normally handle a journey with several legs and price it as one fare, which is often cheaper for the customer and easier to change later than separate tickets. Some budget airline connections do not offer this at all, so the portal has to put the journey together as separate one way tickets. That still gets your customer where they are going, but each leg then carries its own rules for changes, refunds and baggage, and your customer needs to be told that clearly.
There are practical limits worth knowing before you promise it. A search with many legs takes longer to come back than a simple return search, because the supplier has to price every combination. Some suppliers also cap how many legs they will accept in one request, and an unusual routing can come back empty even when the flights do exist.
If this kind of trip is common for your customers, ask which of your connected flight suppliers allow multi city searching and how many legs each one accepts, then try a real routing your customers often ask for on your own portal before you rely on it.