There are cheap USB audio dongles, you could try to hook up as many as you need and configure the audio output of your operating system accordingly. Linux with PulseAudio (recommended), JACK or probably plain ALSA (I doubt that though) should be able to do such kind of broadcast, but the USB bus will be a limitation at some point. Some other problems of USB audio may also occur.
You could look for audio recording interfaces that usually come with more headphone outputs, usually they also have monitoring outputs for low latency. My Behringer FCA610 as 2 of these outputs. You could feed 2 headphones through the monitoring ports and another 3 stereo devices through the connectors on the back without any complicated wiring, but 2 headphones on every output should be possible, not recommended though. There is an FCA1616 and many other affordable recording interfaces with more ports that would fit this need.
Of course there are also HiFi DAC/Amps that deliver more power to demanding headphones. I also have 2 of these (mobile and desktop). Mixing a great variety of different loads to feed them with high(er) power without any calculation, just hoping every load will work ideally has a high risk of getting mixed results or damaging some component.
Since you didn't mention any specific usecase, you could also utilize Bluetooth to connect at least one more device.