Adding a setter to a derived interface

This isn’t a problem:

public interface IReadOnly {
    Data Value { get; }
}

internal interface IWritable : IReadOnly {
    new Data Value { get; set; }
}

internal class Impl : IWritable {
    public Data Value { get; set; }
}

The Impl.Value property implementation takes care of both IReadOnly.Value and IWritable.Value, as demonstrated in this test snippet:

        var obj = new Data();
        var target = new Impl();
        var irw = (IWritable)target;
        irw.Value = obj;
        var iro = (IReadOnly)target;
        System.Diagnostics.Debug.Assert(Object.ReferenceEquals(iro.Value, obj));