There’s no set limit in case you own a premium or a platinum account. However, if you own a free account, you can add only one account per service. Premium & Platinum account holders can associate and backup to multiple accounts on Flickr, Picasa, SmugMug, OneDrive, Dropbox, Box, Facebook, Google Drive, Youtube, Amazon S3, Foursquare and Instagram.
In order to add multiple accounts for a given service, click on the ‘+’ sign that you see in front of the service and then click ‘Add New’ button you see in the message box that appears. Fill in your account credentials and click ‘connect’ button. But remember, only one account can be active at a time. All your photos uploads will be made to this ‘active’ account only.