Can I sign into two Steam accounts on the same PC?

You can't have Steam installed multiple times on the same machine. However, what you can do is enable Family Sharing between the 2 accounts so you always got access to most games on both accounts.

How do I enable Family Library Sharing on my computer?
To enable Family Library Sharing, first be sure you have Steam Guard security enabled via Steam > Settings > Account in the Steam Client. Then enable the sharing feature via Settings > Family, (or in Big Picture mode, Settings > Family Library Sharing,) where you'll also authorize specific computers and users to share.

This won't give access to all games, because the publisher can decide to disable family sharing.