Calling an async method multiple times

Basically, you want to cancel the previous invocation of the Initialize method. And in TPL, if you want to cancel something, you should usually use CancellationToken.

The way you could do that here is to have a field of type CancellationTokenSource in your view model, representing cancellation of the last invocation of Initialize. When you run Initialize, it cancels the previous invocation, sets up its own cancellation, calls the service and then only sets the property if cancellation wasn't requested. In code:

class ViewModel
{
    // default value just to avoid a null check
    private CancellationTokenSource intializationCancellation =
        new CancellationTokenSource();

    public async Task InitializeAsync(int parameter)
    {
        // cancel previous initialization, if any
        intializationCancellation.Cancel();

        var cts = new CancellationTokenSource();
        intializationCancellation = cts;

        var value = await GetValueaAsync(parameter);

        if (cts.Token.IsCancellationRequested)
            return;

        Value = value;
    }

    private async Task<string> GetValueAsync(int parameter)
    {
        // call the external service here
    }

    public string Value { get; private set; }
}

If the service you're calling supports cancellation, you should pass the CancellationToken to it too, which is likely to save some resources. If you do that, don't forget to catch the resulting OperationCanceledException (since I believe you don't want Initialize to throw, even if it's canceled).