Yes, you can. Most itinerary builders let you save a trip you have already put together as a template, then start a new quote from that template rather than from a blank page. For agencies that sell the same few routes again and again, this is usually the single biggest time saver, because the day by day plan, the inclusions and exclusions, the write ups and the photos are the parts that take the longest to type and they almost never change from one customer to the next.
In practice you open the saved itinerary, give it the new customer's name and travel dates, and the days shift along so that the first day of the plan sits on the new departure date. From there your staff change only what is actually different, such as the number of travellers, a hotel the customer does not want, or an extra day added at the end. You can also keep several versions of the same trip, for example a budget version and a premium version, and send whichever one suits the enquiry.
The honest limit is that descriptive content copies over cleanly but live content does not. Anything that comes from a supplier connection, such as hotel availability or flight and transfer costs, has to be checked again for the new dates, because availability and contracted rates change by season and by supplier. The system will not promise you that last month's rate still stands, and you should not quote it as though it does.
It is worth going through your itineraries and seeing which parts are your own written content and which parts depend on a supplier, then saving your best selling trips as templates first and letting your team build the habit from there.