At my current company, all employees have *.com and *.de email addresses. The problem now is that if I search for emails from a certain contact I have to choose between emails from either one of the two. Is there a way to be able to search for both of them at once?
You could write directly the search terms as was suggested in the Alex answer but also Gmail could write if for you.
from:(email@example.com OR firstname.lastname@example.org)
from:(email@example.com | firstname.lastname@example.org)
In Gmail, hover over the email in a message received by the contact that you want to search for all the emails sent by that contact, a contact card popup will be displayed, then click on the Messages link at the bottom of the card.
In Google Contacts, open the contact record, click More > View recent conversations.