No. At the moment, all Paystack accounts added as new businesses to an existing Paystack account are linked to one email address. Changing the login email on one of these accounts automatically changes the login email for all other linked accounts.
However, it is possible to have an additional login email for any of the accounts. To do this, you will need to add your second preferred email as a user on the Paystack account you need more than one logins for, and assign an admin role. Please find more information on how to add a user to my Paystack business?.
Please note that this does not remove this business from the list of businesses on your main Paystack account (See below image). What it does instead is to enable you login to that business using two different email addresses—the one for the main Paystack account and the one you added as a user.