C# - Multiple generic types in one list

This is probably not possible, but I have this class:

public class Metadata<DataType> where DataType : struct
{
    private DataType mDataType;
}

There's more to it, but let's keep it simple. The generic type (DataType) is limited to value types by the where statement. What I want to do is have a list of these Metadata objects of varying types (DataType). Such as:

List<Metadata> metadataObjects;
metadataObjects.Add(new Metadata<int>());
metadataObjects.Add(new Metadata<bool>());
metadataObjects.Add(new Metadata<double>());

Is this even possible?

public abstract class Metadata
{
}

// extend abstract Metadata class
public class Metadata<DataType> : Metadata where DataType : struct
{
    private DataType mDataType;
}

Following leppie's answer, why not make MetaData an interface:

public interface IMetaData { }

public class Metadata<DataType> : IMetaData where DataType : struct
{
    private DataType mDataType;
}

I have also used a non-generic version, using the new keyword:

public interface IMetadata
{
    Type DataType { get; }

    object Data { get; }
}

public interface IMetadata<TData> : IMetadata
{
    new TData Data { get; }
}

Explicit interface implementation is used to allow both Data members:

public class Metadata<TData> : IMetadata<TData>
{
    public Metadata(TData data)
    {
       Data = data;
    }

    public Type DataType
    {
        get { return typeof(TData); }
    }

    object IMetadata.Data
    {
        get { return Data; }
    }

    public TData Data { get; private set; }
}

You could derive a version targeting value types:

public interface IValueTypeMetadata : IMetadata
{

}

public interface IValueTypeMetadata<TData> : IMetadata<TData>, IValueTypeMetadata where TData : struct
{

}

public class ValueTypeMetadata<TData> : Metadata<TData>, IValueTypeMetadata<TData> where TData : struct
{
    public ValueTypeMetadata(TData data) : base(data)
    {}
}

This can be extended to any kind of generic constraints.