The last update (4.00) of the PS4 allow users to open Spotify while ingame.
This option is something I was waiting, but I dislike streaming music.
Is it possible to do the same with local music played from the Media Player app?
According to the Playstation 4 Owners Manual, yes, using the USB Music Player.
Your PS4™ system can play music files from a USB storage device. You can listen to music in the background without interrupting games, the Internet Browser, or other applications.
- Use your computer to create a folder called "Music" on the USB storage device.
- Copy your music files to the "Music" folder.
- Connect the USB storage device to your PS4™ system.
- Select (Library) in the content area.
- Select (USB Music Player) in the content area.
- Select the music you want to play.
To play all of the music in the folder, highlight the folder, press the OPTIONS button, and then select [Play].
However, it seems that some applications will stop the music playing. Bear in mind the following section:
Supported file types MP3 AAC
FAT and exFAT formatted USB storage devices are supported. It might not be possible to play some files due to their data type or file size. This application will not play copyright-protected music files. Some types of content distributed over the Internet and by other means have playback restrictions. For details, contact the content provider.