Remove/add MessageHandlers at runtime

How can I add or remove message handlers at runtime? The following example does not work:

var logHandler = GlobalConfiguration.Configuration.MessageHandlers.FirstOrDefault(a => a.GetType() == typeof(ApiLogHandler));

if (logHandler == null)
{
    GlobalConfiguration.Configuration.MessageHandlers.Add(new ApiLogHandler());
}
else
{
    GlobalConfiguration.Configuration.MessageHandlers.Remove(logHandler);
}

The message handler is added to the list, but it is not called in the the next requests...

I would inject a MessageHandler into the configuration at startup that is built specifically to have a dynamic list of inner message handlers, and change the interface they use from DelegatingHandler to a custom one, e.g.

public interface ICustomMessageHandler 
{
    Task SendAsync(HttpRequestMessage request, CancellationToken cancellationToken);
}

After this, you can create a standard MessageHandler that contains a list of inner handlers:

public class DynamicMessageHandler : DelegatingHandler
{
    public List<ICustomMessageHandler> InnerHandlers { get; set; }

    public DynamicMessageHandler()
    {
        InnerHandlers = new List<ICustomMessageHandler>();
    }

    protected override async Task<HttpResponseMessage> SendAsync(HttpRequestMessage request, CancellationToken cancellationToken)
    {
        foreach (var innerHandler in InnerHandlers)
        {
            await innerHandler.SendAsync(request, cancellationToken);
        }

        return await base.SendAsync(request, cancellationToken);
    }
}

This way youshould be able to modify the list of InnerHandlers at runtime as long as you keep a single instance of DynamicMessageHandler around.