You cannot change the TypeConverterAttribute to add something to it, but you can add any number of custom attributes to the property, so you can create your own attribute to hold custom data.

Here is some sample C# code:

public class Animals
{
    // both properties have the same TypeConverter, but they use different custom attributes
    [TypeConverter(typeof(ListTypeConverter))]
    [ListTypeConverter(new [] { "cat", "dog" })]
    public string Pets { get; set; }

    [TypeConverter(typeof(ListTypeConverter))]
    [ListTypeConverter(new [] { "cow", "sheep" })]
    public string Others { get; set; }
}

// this is your custom attribute
// Note attribute can only use constants (as they are added at compile time), so you can't add a List object here
[AttributeUsage(AttributeTargets.Property, AllowMultiple = false)]
public class ListTypeConverterAttribute : Attribute
{
    public ListTypeConverterAttribute(string[] list)
    {
        List = list;
    }

    public string[] List { get; set; }
}

// this is the type converter that knows how to use the ListTypeConverterAttribute attribute
public class ListTypeConverter : TypeConverter
{
    public override bool GetStandardValuesSupported(ITypeDescriptorContext context) => true;

    public override StandardValuesCollection GetStandardValues(ITypeDescriptorContext context)
    {
        var list = new List<string>();

        // the context contains the property descriptor
        // the property descriptor has all custom attributes defined on the property
        // just get it (with proper null handling)
        var choices = context.PropertyDescriptor.Attributes.OfType<ListTypeConverterAttribute>().FirstOrDefault()?.List;
        if (choices != null)
        {
            list.AddRange(choices);
        }
        return new StandardValuesCollection(list);
    }
}