Etiquette for taking on a new coach?

Hi all, I recently tried to take on an additional coach and fear that I may have stepped on some toes in the process.Background: I’ve been with the same coach (let’s call her “Anna”) for about half a year, since she was my instructor for group lessons. Anna and I get along really well, and have made a lot of progress – she has taken me through my singles except the axel. Unfortunately, she is still a student, and is prone to changing our practice schedule when mid-terms and finals come around. Recently, Anna has canceled on me numerous times, sometimes at the last minute (after I have already made the 50-minute trip to the rink), and so I haven’t had a real lesson in about 1.5 months. It’s a little frustrating, especially since the things I’m working on like spins, etc. are hard to improve without a coach’s feedback.So I’ve been looking around for an additional instructor – not to replace Anna entirely, since I do like her and want to keep working with her, but to be there when Anna can’t take me and to give me experience working with someone else. My rinkmates gave me good reviews of another coach at our rink (let’s call her “Beth”), so I approached her at the rink on Monday, and was able to schedule an initial lesson this week.It was only afterward, when I texted Anna about my schedule and mentioned the lesson with Beth, that I realized that I may have gone about this incorrectly. Anna seemed very supportive and open to coaching me alongside Beth, but I want to ask for future reference:Should I have asked Anna’s permission first? How do people normally go about this?Is it ok to have multiple coaches? Could this lead to conflict?Do I get more leeway in negotiating this as an adult skater?I would love to hear your feedback 🙂