I would move all object construction logic into a different class using the Factory_pattern.

In @MattDavey example the class Outer knows how to create items of type Inner.

(example in c#)

public Outer()
{
    _inner = new Inner();
}

I would change this to

public Outer(Inner inner)
{
    _inner = inner;
}

and let the factory create Outer items for you:

public class OuterFactory
{
    // Existing behaviour - concrete Inner instantiation is hard coded
    public virtual Outer createOuter(CreationParameters parameters)
    {
        Inner _inner = createInner(parameters);
        Outer outer = new Outer(inner);
        
        return outer;           
    }

    public virtual Inner createInner(CreationParameters parameters)
    {
        Inner _inner = new Inner();     
        return _inner;          
    }
}

If you need a different inner class you can easily create a new factory that derives from the base factory:

public class MySpecialOuterFactory : OuterFactory
{
    public overrrde Inner createInner(CreationParameters parameters)
    {
        Inner _inner = new SpecialInner();      
        return _inner;          
    }
}

I would move all object construction logic out of Outer into a different class using the Factory_pattern.

The Constructors of domain-classes ´Outer´ and ´Inner´ get all required child parameters

public Outer(Inner inner)
{
    _inner = inner;
}

and the factory create the items for you:

public class OuterFactory
{
    // Existing behaviour - concrete Inner instantiation is hard coded
    public virtual Outer createOuter(CreationParameters parameters)
    {
        Inner _inner = createInner(parameters);
        Outer outer = new Outer(inner);
        
        return outer;           
    }

    public virtual Inner createInner(CreationParameters parameters)
    {
        Inner _inner = new Inner();     
        return _inner;          
    }
}

If you need a different inner class you can easily create a new factory that derives from the base factory:

public class MySpecialOuterFactory : OuterFactory
{
    public overrrde Inner createInner(CreationParameters parameters)
    {
        Inner _inner = new SpecialInner();      
        return _inner;          
    }
}