There will definitely be students from other houses that you want on your team, and luckily you have the option to persuade almost any student to join your house. As long as one specific stat (like attack or speed) and skill (such as sword, authority, or horse riding) of Byleth is high enough, you can bring the student you want into your own house. (You can find the required skills and stats for each student at 1:13 in the video.)
What the game doesn't tell you is that your stats and skills can be lower when you have a support with the student from the other house. From a C-support level, you can convince them with much lower stats and skills, and from a B-support level, they will almost immediately come to your house, even if you don't have the necessary stats or skills!
You might be wondering how to get a support with students you don't even have. Well, you can ask other students to help you with the mission of the month; they will assist you throughout the month and also in battles you do on the weekends. During those battles, make sure the student stays close to Byleth. Ensure that they heal each other often or start battles while standing next to each other. This way, you'll quickly be able to bring any student you want into your house! Is it a bit too confusing for you? Then take a look at the video below!