how to redirect to another site but still have same url Is it possible to have an entire path from a drupal 7 site , eg. /externalpaths  which will go to an outside application, yet still have the same domain name in the url, so that it looks like you have not left the drupal site ?
You should be able to do that relatively easily with full HTML mode using an &lt;iframe src='desiredurl'&gt;&lt;/iframe&gt;. You will most likely want to do some custom styling/template editing to make it look good.

Whether that is a good soluton for you depends a bit on how you want it to look etc. Do note taht security restrictions can break it - and make custom scripting/styling problematic as well inside the iframe. I'd suggest reading the Mozilla Dev Network's iframe page.