Currently, performing consecutively paste operation does not work like in TextBox. 
In TextBox the strings are concatenated but in MaskedTextInput the caret is in the beggining and only the first paste is successful.

The XAML team has recently reviewed the status of this feature request and will not be addressing it in future.
Consecutive Paste operation works in No-Masked scenario (Set Mask=""). Changing the paste behavior in masked scenarios would be a breaking change for some of our clients.