Is it legal for three companies that issue music license to force me to purchase a license from each one? If not, what can I do?

I would need more details about what you are talking about. Is your business a music venue and are you being forced by PROs, or performing rights organizations, to buy performance licenses? The main PROs are ASCAP, BMI, and SESAC, and to play their repertoire, live or recorded, in most venues, they require the venue to purchase their licenses. The licenses supposedly go to pay the songwriters and their publishers, with the overhead of running the PRO. If this is what you are asking about, yes, they can do this, since the songwriters have joined the PROs. One way to avoid such licensing and still have music is to contract with a company that licenses royalty-free music. Those companies provide packaged music that is fully cleared for use with no further payments. The companies often offer to select music suited for your business. Many chain restaurants, stores, airlines, and health clubs have such music. With such services, you are not getting the latest hit songs and you don't get to hear whatever you want. But you do get solid, good music for your business at one price, with no threats or hassles. I hope this answers your question.

You will need to pay for licenses from each company to play the music of the artists that company represents. If you can limit your music choices to the artists represented by just one of the companies, you will only need to pay for that license.