If the account doesn't need a signature, assign a blank signature to it. To do so, create a blank signature that contains 2 dashes and a space ( -- ) to use when you don't want to use a signature. When no signature is assigned to an account the signature feature is completely removed from the message and changing accounts will not update the signature.
Outlook 2010, Outlook 2013, Outlook 2016
Provided you have assigned a signature to the currently selected account, Outlook will change the signature when you select a different account from the Account dropdown
To set the signatures for each account, go to File, Options, Mail, Signatures and create your signatures then assign one to each account in your profile.
Always assign a signature to accounts, using the blank signature on accounts that don't need a signature. When you use an account that has no signature assigned ("<none>") signatures won't be used when you change accounts and you can't right click add a signature to the message.
Provided you have assigned a signature to the currently selected account, Outlook 2007 will change the signature when you select a different account from the Account dropdown
Go to Tools, Options, Mail format, Signatures to create new signatures and assign them to each account in your profile.