You cannot change the mode once the page is loaded. And you cannot change it programmatically. The only way to force a page into quirks mode is to load it without a valid doctype or with serious bugs in the HTML.
If you have a doctype, but your page is still loading in quirks mode, then it means that you have serious bugs in your HTML. This will give you bigger problems than just being in quirks mode. You should definitely fix those bugs. If you really want to be in quirks mode, drop the doctype, but you should really try not to have HTML code that is so bad it triggers quirks mode even with a doctype!
You can validate your HTML to find those bugs by using the W3C validator.
In terms of switching your page at runtime between IE10's two different quirks modes, the simple answer is that you can't do that.
Sorry about that.
However, to be honest, it's probably for the best. Using quirks mode is be a complete disaster anyway. It doesn't just change the layout mode; it also switches off most of the browser's features (ie pretty much everything invented since 1998).
But now for the good news:
Luckily, switching away from Quirks mode is a lot easier than you think.
The main layout issue (the different box model) can be fixed by adding the following to the top of your CSS:
*{box-sizing:border-box;}
This is the standards-compliant way to set the box model to the quirks-mode style layout. Most of the broken layout problems cause by switching from quirks mode to standards mode can be resolved with this simple CSS style.
There are other quirks, but they're relatively minor and shouldn't be too hard to deal with once you've fixed the main issue. A lot of them are actually not quirks mode issues, but bugs in older IE versions that the original coder may have had to hack his way around. There's no guarantee that these will continue working the same in future versions anyway, even if you do stick to quirks mode, so you would be best off fixing them now anyway.
So, to summarise:
- Fix your page so it loads in standards mode. Valid doctype and valid HTML.
- Use
box-sizing
to mitigate the main layout gremlins caused by the switch. - Fix the remaining layout issues manually.
It's really a lot less work than it sounds. Honest.