You can add several videos into one player on your web page with a Multiple Video Player Shortcode:

multiplevideo-1
Open the shortcode editor to add links to self-hosted videos. For a crossbrowser compatibility you need your videos to be in 2 formats – mp4/m4v, ogg/ogv.
multiplevideo-2

 

Shortcode performance in different themes:

 
This shortcode is available in all themes with identical functionality