The only difference between DTE and MTE is the fact that MTE has an end entry character so it can be variable in length.
What does that mean for your routine? Not much. It's simple. When your code jumps to what would have been a DTE entry writes two characters and returns, you'll change that bit of code to write characters until it hits the end entry character and then return.
That's why I never understood why anyone uses DTE anymore. MTE is compatible with DTE and encompasses so much more. And it barely takes anymore code to do.
As for how to implement it in your game. Take a step back and think about what you're doing. Forget about individual lines of code. What are you doing on a conceptual level? The details of your text engine don't really matter.
1. You need to recognize an MTE entry. If the game already does this, you can work with it, or you can make the game recognize a new value for MTE entries. Let's say it's 0x45. So anytime, you see a value 0x45 in the text routine, you best be jumping out to the MTE routine.
2. In the MTE routine, you'll load the next value after 0x45 which is your MTE entry. You'll use that as an index to a table(or as an entry counter if you want to do lookup that way). You'll find the MTE entry in the table. You'll print characters in that entry until you hit an end entry byte which can be whatever you want it to be.
3. Now you return back to the original routine make sure your text pointer is at the correct entry and go on as normal.
That's all you're doing. The only real work is figuring out where to insert your code into the existing game routines. Any decent debugger will help you figure that out. You'll want to start by inserting your MTE byte recognition in the main text routine after it loads the character. You'll want to stick your main MTE routine anywhere there is accessible free space.
As for finding the existing MTE tables. Well, you can take the information I just gave you and use a debugger and trace the code. Should be VERY easy that way if your skilled enough to use one. The other way is to examine the text. Figure out what a specific MTE entry is and search for it in the ROM. If you've got the right location, you can edit that text and see it change in the game everywhere it's used.
Then you know you've found your table. The you can examine it and see how it is set up. Each entry probably has an end entry marker. There may or may not be a master pointer table. It will be something along those lines. If you can find where the table is, you'll understand how it works with a bit of investigation.