More Than Three Weeks?
If you are lucky enough to have longer than 3 weeks to spend on your Egypt vacation then you have plenty of time to plan it for yourself.
One thing you could do is take a look at the 2/3 week route itineraries and make some additional stop.
For example you may want to see the Siwa Oasis out in the Western Desert near the Libyan border. Or perhaps spend a night or two in Alexandria.
If you like the beaches of Sinai there are plenty more stops to make along the coast between Sharm El Sheikh and the Israeli border,
Alternatively you might want to consider some form of activity while you're in the country. You could volunteer, study Arabic, or complete a diving certification.
Anyway, with more than three weeks at your disposal you have plenty of time to think about it.
Enjoy!
