Unable to make a serializable XUnit test class with OutputTestHelper

Question

Is it possible to make an Xunit class using IOutputTesthelper (or any mean to generate output) and inheriting from IXunitSerializable in order to have the test cases show up as individual tests?

One way to create an Xunit class that uses IOutputTesthelper to generate output and inherits from IXunitSerializable is to implement the Serialize and Deserialize methods of the interface. This allows the test cases to be serialized and deserialized by the test runner, and to appear as individual tests in the test explorer.

For example:

public class MyTestClass : IXunitSerializable, IOutputTesthelper
{
    public string Name { get; set; }
    public ITestOutputHelper Output { get; set; }

    public MyTestClass() { }

    public MyTestClass(string name, ITestOutputHelper output)
    {
        Name = name;
        Output = output;
    }

    public void Serialize(IXunitSerializationInfo info)
    {
        info.AddValue(nameof(Name), Name);
    }

    public void Deserialize(IXunitSerializationInfo info)
    {
        Name = info.GetValue<string>(nameof(Name));
    }

    [Theory]
    [InlineData("Alice")]
    [InlineData("Bob")]
    public void TestName(string name)
    {
        Output.WriteLine($"Hello, {name}!");
        Assert.Equal(Name, name);
    }
}

But this won't work since a test class should only define a single public constructor.