Solution 1:

Yes, just code against the base Enum type, e.g.

public static void Something(this Enum e)
{
    // code here
}

The down-side is you'll probably end up doing some quite nasty stuff like finding the real base type using Enum.GetUnderlyingType, casting, and going down different branches depending on what the base type of the enum is, but you can find some good uses for it (e.g. we have IsOneOf and IsCombinationOf methods that apply to all enums).

PS: Remember when writing the method that, although ill advised, you can use float and double as the base types for enums so you'll need some special cases for those as well as unsigned values.

Solution 2:

Yes, you can. The target extenstion type is of type Enum. In C#, this would be done as:

public static void EnumExtension(this Enum e)
{
}

or like this in VB:

<Extension()> _
Public Sub EnumExtension(ByVal s As Enum)
End Sub