DelegatingHandler for response in WebApi

Yes. You can do that in the continuation task.

I explain it here.

For example, this code (from the blog above) traces request URI and adds a dummy header to response.

public class DummyHandler : DelegatingHandler
{
    protected override async Task<HttpResponseMessage> SendAsync(HttpRequestMessage request, CancellationToken cancellationToken)
    {
        // work on the request 
       Trace.WriteLine(request.RequestUri.ToString());

       var response = await base.SendAsync(request, cancellationToken);
       response.Headers.Add("X-Dummy-Header", Guid.NewGuid().ToString());
       return response;
    }
}