What next?

The next step would be a streamer and DAC. Sounds like you are talking a very low budget. Have a look at a BlueSound Node X. This should be a huge jump in performance. 
 

The more you spend (assuming careful choosing) the better sound you will get up to the limit of your amplification / speakers. If I was in your situation I would go as far as a Schiit Yggdrasil (no I am not joking) DAC, and a used Aurrender N100 (or better yet N150) Streamer. That is my guess about where you would be enjoying the best sound  quality from your system. Which should be far far better than what you get now. Using an iPhone as a source is pretty much the lowest level.

Agree your next move should be a streamer and DAC.  Not sure what your budget is, but you could get a highly-regarded iFi Zen Stream and Musician Draco DAC for about $1000 and be at an entirely higher performance level.  I started streaming with my iPhone, but when I added the Zen Stream my streaming sound quality went to another level entirely — not even close.  Best of luck.

Thanks for the replies, will be researching them.

BTW, what is your budget and would you want new or used?

You are so far getting fantastic advice…. ditch Apple music as fast as possible…