One approach is to have two video elements and players on your page - this approach is often used for pre, mid and post roll adverts, which are often from a different source than the main video itself.
The two video elements are in the same place on the page, one over the other.
You play the first video and when you are near the end of it preload and then pause the second video but keep the player hidden.
At the point where the first video ends, you hide the first player and show and start the second player.
You then again preload and pause the next video in the player you have just hidden and it becomes the one ready to start when the one now playing is finished.
The snippet below hides the second video until the first has ended and then plays the second one hiding the first. This is just a rough outline you can play with where you cue the movies to etc. If you leave your pointer over the video you can watch the timeline - films fade in and out so it may not be obvious it is playing.
Hover over the video ion the snippet while it is playing to see the time as it switches from one to the other.
var vid1 = document.getElementById("MyVid1");
var vid2 = document.getElementById("MyVid2");
vid2.style.display = "none"
vid1.onloadeddata = function() {
vid1.currentTime = 872;
vid1.play()
};
vid2.onloadeddata = function() {
vid2.currentTime = 10; //Just to illusrate as begining is black screen
vid2.pause()
};
vid1.onended = function() {
vid2.play()
vid1.style.display = "none"
vid2.style.display = "block"
};
<video id="MyVid1" width="320" height="176" controls preload="auto">
<source src="http://peach.themazzone.com/durian/movies/sintel-1024-surround.mp4" type="video/mp4">
Your browser does not support this video format
</video>
<video id="MyVid2" width="320" height="176" controls preload="auto">
<source src="http://ftp.nluug.nl/pub/graphics/blender/demo/movies/ToS/tears_of_steel_720p.mov" type="video/mp4">
Your browser does not support this video format
</video>