You can't do that directly no. The only way I can think of doing this is to extend your object to include a reference to itself as a readonly property:
Public Class TextBoxExtended
Inherits TextBox
Public ReadOnly Property ObjRef As TextBox
Get
Return Me
End Get
End Property
End Class
You can then do this in your with Block:
With myObj
.thisMethod()
someFunction(.ObjRef)
.thatMethod()
End With
However I would have to question why you would want to do this.