How to, using dependency injection, get configuration from multiple sources?

I'm using Simple Injector, but maybe what I need is more of a conceptual answer.

Here's the deal, suppose I have an interface with my application settings:

public interface IApplicationSettings
{
    bool EnableLogging { get; }
    bool CopyLocal { get; }
    string ServerName { get; }
}

Then, one would usually have a class which implements IApplicationSettings, getting each field from a specified source, for instance:

public class AppConfigSettings : IApplicationSettings
{
    private bool? enableLogging;
    public bool EnableLogging
    {
        get
        {
            if (enableLogging == null)
            {
                enableLogging = Convert.ToBoolean(ConfigurationManager.AppSettings["EnableLogging"];
            }
            return enableLogging;
        }
    }
    ...
}

HOWEVER! Let's say I want to get EnableLogging from app.config, CopyLocal from database, and ServerName from another implementation which gets the current computer name. I want to be able to mix-match my app configuration without having to create 9 implementations, one for each combination.

I'm assuming that I can't pass any parameters because the interfaces are resolved by the injector (container).

I thought of this, initially:

public interface IApplicationSettings<TEnableLogging,TCopyLocal,TServerName>
where TEnableLogging : IGetValue<bool>
where TCopyLocal : IGetValue<bool>
where TServerName : IGetValue<string>
{
    TEnableLogging EnableLog{get;}
    TCopyLocal CopyLocal{get;}
    TServerName ServerName{get;}
}

public class ApplicationSettings<TEnableLogging,TCopyLocal,TServerName>
{
    private bool? enableLogging;
    public bool EnableLogging
    {
        get
        {
            if (enableLogging == null)
            {
                enableLogging = Container.GetInstance<TEna