I like to think of extra FPs as bonus rides or time saved in my plan, instead of counting on them. Make your plan without them, and then get them if you can. As soon as you tap your MBs at the entry to your third FP, you can look for new ones. I find it tricky to do it while walking in line towards the attraction, but it can be done!
Yes, you’ll have to adjust what you’re doing to use the new ones. It does tend to flow logically once you see what’s available and choose the best looking one - hopefully something you actually want to do that’s maybe not to far away and at a reasonable time. If you have a vague idea of where things are, that can help you minimize walking.
If you want to optimize your plan in the parks, you just do the new FP (without entering it into your plan.) Then take the time to mark everything you’ve finished as “done” and optimize what’s left of your plan when you’re ready to start again. If you prefer to use a printed plan and not let the software re-order things, then it might be a good idea to build a couple of 15 minute break times into the afternoons so that you can do the other things in your plan around new FPs without getting too far off track.