What's the best way to advertise in a saturated market?
You have to distinguish yourself from your competition. It's the only way you will end up with a client list that you won't be able to handle because of referrals.
And hopefully if you have a good relationship with a few of your competitors you can refer back and forth--eventually to everyone's benefit.
I have seen massage therapists create work groups that become like an association or guild of professionals that offer different specialties through their group. This enables them to refer the same client back and forth according to what that client may need for their next appointment.
If you want to just market you, get yourself out of the crowd. Make yourself known by some kind of notable feature that you are or have.
I knew a guy who was known as the "Golden Hand." Can you guess how many clients he had?
Again, what sets you apart is not only your talent and ability but also how are you remembered. This lends to personal branding--what do people remember?
Once you've set yourself apart as a true professional in your field not only will clients refer to you, but colleagues will too.