Escalations .... I would like to send an escalation email to the tp!assignees as

The toemailrecipient() function should be able to help you use multiple parameters in the send field.

forum.appian.com/.../Conversion_Functions

@biancad, fn!toemailrecipient(tp!assignees,<list of other emails>)

Thanks for you help @steven.miccile and @sikhivahans .... I have tried both options and I have realized that my problem not be able to be solved without creating a "dummy" user with the email address I want to send to.

The Send Escalation Alert field wants receipients (users). However, I want to send to an email that is not associated with an user in the system. After trying to send the escalation to just an email address I get the following error message "You must enter recipients for this alert."

I'm trying to avoid creating a user for this problem

@biancad To my knowledge, recipients field in the send alert of the escalation tab either expects an user or a group(who are an internal part of Appian). I suggested fn!toemailrecipient keeping the email in mind(as asked by you initially. I think even steve.miccile might has suggested in the same manner.)

Your escalation could send a message to trigger another process to start and in that process, you can use the send email smart service to a list of users and/or email addresses.
forum.appian.com/.../Escalating_a_Task and
forum.appian.com/.../Send_Message_Event

Yes, I misunderstood your use case. Escalation events can send alerts but not emails (although, users may have their alerts emailed to them based on alert settings). Terri's suggestion should fit your requirements.