The only way is to sign out of one and then sign into the other. Here’s how:
- Click Sign Out just below “Hi, yourname” at the top of the page.
- This returns you to Yahoo!’s home page. Here, click Mail to sign into the other account.
Using more than one account: You can use the same computer for multiple Yahoo! Mail accounts, but it isn’t possible to be signed in to more than one account at a time in the same browser.
If you have two different browsers on your computer—for example, Firefox and Internet Explorer—you can open both browsers to sign in to two different accounts.[source]