Does Simple Injector have a way to Register with an instance factory in combination with a TypeFactoryContext?

I'm working on a legacy code base that seriously needs refactoring towards SOLID principles. We are adding the Simple Injector dependency injection container to the mix as a first step.

For one of the registrations I need something very much like the RegisterConditional example for Log4Net, i.e:

container.RegisterConditional(
    typeof(ILogger),
    c => typeof(Logger<>).MakeGenericType(c.Consumer.ImplementationType),
    Lifestyle.Singleton,
    c => true);

Difference is that I want to inject an instance returned by a factory method that takes the c.Consumer.ImplementationType as input:

container.Register???(
    typeof(ILogger),
    c => LoggerProvider.GetLogger(c.Consumer.ImplementationType),
    Lifestyle.Transient);

Can this be accomplished in Simple Injector?

I have read the answer to a similar question, but that does not suffice. The ImplementationType needs to be handed to the instance factory.

For the time being, I will implement a Logger<TParent> and use that in the RegisterConditional call:

public class Logger<TParent> : ILogger
{
    private readonly ILogger _decoratedLogger;

    public Logger()
    {
        _decoratedLogger = Logger.GetLogger(typeof(TParent));
    }
}