No, this is not possible. You can only have one theme activated at any given time.
However, you can add as many page templates to a single theme as you want. They just need to be in separate files. For example, my theme contains:
page.php← Standard page templatepage-archive.php← Page template for special archive pagespage-blog.php← Page template for a custom blog pagepage-landing.php← Page template for special marketing campaign landing pages
You can build any hierarchy you want, so long as each page template file includes the regular page template header:
<?php
/*
Template Name: About Page
*/
?>
... The rest of your regular template file continues below ...