No, sorry. You cannot use more than one Apple ID at a time on an iPhone. If you choose to sign out, and associate a new Apple ID with the device, the previous ID will be locked out for 90 days from the device.
Though not sure how that relates to logging into a Blog, or sharing bookmarks from it. The blog would have its own account and generally be separate from the Apple ID on the device.
Also, the social media Apps are independent from your Apple ID. You can change accounts in the apps at any time. Your Apple ID should not be involved in that. Each app should have its own way of switching accounts or logging out of the current account and logging in with a different one.