Final answer:
You cannot directly modify the page header after it has been sent in Apex. Possible workarounds include using Apex's ajax-based functions like apex:actionFunction or apex:remoteAction to send a new request or leveraging Visualforce components for dynamic page content.
Step-by-step explanation:
The question seems to be asking about modifying HTTP response headers in Salesforce's Apex programming language after the HTTP page header has been sent. In a web application context, once the header has been sent to the client, you usually cannot modify it because it's the first part of the response that a server sends to a client's request. However, in Apex, there are some workarounds like using JavaScript to modify the client-side state or appending additional data to the response body that can be interpreted by the client.
In specific Apex scenarios, if you wish to add or modify headers after the page has already been partially rendered, you might consider using Visualforce's apex:actionFunction or apex:remoteAction to initiate a new request that can carry the new or modified headers. It's important to note that these are client-side calls that lead to a server-side action, and they are part of Ajax-based solutions in Salesforce. An alternative, though less commonly used method, would be to leverage Visualforce components that allow you to render parts of the page dynamically. This would not send headers per se but would allow for changes in the displayed content after the initial page load, which could emulate the result of what you might have achieved by sending different headers.