Yes, you can usually save a trip you have already built and use it again as the starting point for the next customer. Most itinerary builders have some form of template or duplicate option, so a tour you put together once can be copied, given new dates and a new traveller name, and sent out again in minutes instead of being rebuilt day by day.
What copies across is the shape of the trip. The day order, the sightseeing and transfer items you created yourself, the written descriptions, the photos and the inclusions and exclusions normally come over as you left them. What does not copy is live pricing and availability. Anything that comes from a supplier API, such as a flight or a hotel room, has to be searched again for the new dates, because the old rate belonged to the old booking and the supplier will not honour it. Your own services are simpler, since you set those prices yourself, though you should still review them if some time has passed.
There are limits worth knowing. Whether a template can be shared with your whole team or only with the person who made it, and whether editing a template changes the trips already sent from it, differ from one system and plan to another. Date shifting varies too, as some builders move every day forward when you change the start date while others leave you to adjust a few things by hand.
The sensible next step is to take one of your real itineraries, ask for it to be saved and reused in a demo, and watch closely what the system fills in for you and what it leaves blank.