If you really want to make more money you teach mass classes. When I was in Germany I sat in on a music class in Fulda where there where 3 students and one teacher. The teacher shared his attention amongst the three and charged about $90 AUS for the hour for each student. $270 an hour is quite a good pay if you ask me for teaching music (although I have paid up to $500 an hour with top teachers).
The difficulty is being able to divide your time to effectively teach multiple students. I was watching this teacher work it was amazing, he didn't let any of the three students stagnate not knowing what to do next, he kept the ball rolling for each of them which I think is very important. I have seen mass classes where it is totally disorganised and students sit there twiddling their thumbs waiting for their teacher to give the next direction, this is poor service imo and not worth much.
You need a lot of teaching experience to be able to teach multiple students effectively. Also you would need a music school to set up this kind of situation unless you have multiple pianos in your own home. Teaching on digital pianos could also be a solution but only for Beginner/Intermediate students. There is a Piano Lab at the Curtin Univeristy here in West Australia, there is about 30 digital pianos all connected up to the teachers seat so he/she can flick a switch and listen to each student individually. There is also a microphone so the teacher can speak to each students seperately without leaving their seat. However I don't know how this would help when teaching fingering or cultivating an efficient technique.
I had one teacher talk with me about how to increase your musical network. This fellow has been teaching guitar for 20 years and like most teachers has reached a limitation to what he can do with his students. When he organises student concerts there simply isn't enough people to fill a hall so he does the concerts in his own backyard, although he has always dreamt about doing it in a public concert hall. "So what do I do about it? How can I get a concert hall filled for my student concerts?" he asked me.
We started to throw ideas around but I was certain to fill the hall you would need to do the concert with a few more teachers and their students. Why does it only have to be your own students? Why can't you get more students from different teachers and who play different instruments? I said if we both do one together (although I have done my own concerts with my students and filled halls) we could easily get it going. Also I encouraged him to speak with his own guitar mentor to try and get some higher class players to support the event.
Getting more teachers with their student networks involved in a mass public concert is a complicated task and might overwhelm those who have little/no experience in setting up concerts. I rely heavily on my experience of doing my own solo concerts, but when we do concerts with several teachers the work needed to get everything working perfectly increases.
People are so lazy (this is not being insulting but its true) most people will not go that extra mile to help you out, they simply do what they need to do and thats it. Any problems the come up before/during the concert they do not mention it to you (like a student not totally commited to be part of the event), so when it comes to the day you have several peformers who magically dissapear and are no where to be found. What do you do then? Also what do you do about rehersing the event? It is quite difficult to get say 30 people who are doing the event to come together, so how do you make sure that you can work out the logistics of the entire event with some people missing?
Unexpected things constantly happen and you will lose a lot of hair over it if you cannot see the solution, but if you have a desire to do this you must work damn hard and have the leaders of the other musical networks to be as inspired to do the same. If you find yourself controlling everyone, including the teachers who organise their own student to play in the student concert, you will find you will spread yourself too thin. You must make sure you work with people who are willing to work hard WITH YOU and go the extra mile. Those who can do things without being ask, or those who are confident that they can do something without having to ask you!
So you can tap into peoples own musical networks and ask them to combine it with your own. This is a powerful tool in getting yourself known. When I do public concerts with my students I am more nervous about them playing than myself. Why? Because the students are a product of my teaching, all of my efforts are highlighted when a student gets on stage to play. From public concerts with my students my name gets better known and people can see the results from my efforts through my students. However how you actually present the concerts itself is important but that is a totally different discussion and quite a personal matter. I try to make the audience realise that all performers bar the teachers, are amateur players, some have never played on stage before so please be kind to them etc etc. I usually start with the "weakest" players first and gradually build up to the best.
Doing student concerts is the next step for those who have saturated their teaching limitations. It is essential to get your students out there to play for the public otherwise all your efforts are simply done behind closed doors (which is fine if that is your aim). Even if you help the student to attain their masters degree in music what is the point if you never present that to the public? It is a paper awarded behind closed doors. I am so proud of my students and encourage them always to give their music (once they do a good job of it) to the public. Some are petrifed to do so, so I feel it is my duty to give them courage even if it means standing next to them on stage while they play.
Giving free public master classes is also important for the music teacher who wishes to expand. Give one free public music class every month. You can do this at a school, church, social club, wherever you think is appropriate. If you give this to say 50 participants if one of them wish to study then you can sign them up. But what about if you cannot handle any more students? Then you pass these prospective student to your star student who is able and willing to teach. You can earn commission out of this of course. Personally I have three students who teach music for a living, they are always willing to have more students (and some of them even have students who teach as well!).
I have drawn out a tree diagram of my student network, it goes down to four level that is... Me (and the teachers I associate with) on level one , the students I teach on level 2, the students of my students level 3, and the students of my students students level 4

It is important to visually see a tree diagram of your students or some sort of diagram which represents your student network. If you can actually see it you can actively change and expand it, don't keep it in your head.
All in all, you can make a lot of money being a music teacher, but you have to break free from thinking about doing it all by yourself. You will reach a maximum student load and simply stay there for the rest of your life if you try that. You must know how to teach your students to teach other people. Even if your student is a professional in another job you should encourage those who are able to at least have a few students every week.
Of course you will know who is suitable to teach or not, I only have 3 students of my own who are capable to teach most levels (except concert pianist level), yes there are other but I do not believe they can teach every level, perhaps beginner/intermediate. It is good to start somewhere, if you have a student who could teach a beginner/intermediate then get them to do it but I personally think a beginner is the hardest student to teach because there are so many hurdles and some simply "do not get it". If a teacher does not know multiple ways to teach a simple concept then they will fail as a teacher. I am always wary of that when I delegate students to one of my own students. Do I think that the problems facing this new prospective student can be solved by my own student? I work this out by interviewing the new student first and measing their musical ability. If they are really good I will teach them myself, if they are not so good then I will give them to one of my other students.
There are more ways to grow your own musical network but in the end you will find that you really need a head quarters, somewhere where all of your students can meet in one place. You will know when you reach that level and the need for that is there. What is the point starting a music school with only 20 students under you? If that is it you will suffer a long hard road to encourage more. But if you start the school and over 100+ music students know you and 1000+ talk about you with the the students you teach then you are getting somewhere. Do more of your own solo concerts, go to primary/high schools and give music to them for free. If you do things for free you still get something out of it, nothing is free. Doing free stuff is simply advertising yourself, not in a scattergun approach (like on radio or television) but focusing your advertising in niches which will be interest to hear from you. Find out where the musical appreciation courses are in your town, get in contact with other music teachers in your area (yes some will be totally arrogant and uninterested in you wanting to bring together your networks, don't waste your time with them let them stay in their little teaching zone for the rest of their lives, just move on to the next one)