The yeast strains don't have to be consistent, but you should use something neutral for the second addition if needed.
I have never added additional yeast but I heard from White Labs directly that adding yeast to an existing already fermented beer might not work unless that yeast is actively metabolizing sugar. (I.e. make a starter and add when active.) Otherwise you could dump in yeast and it might just settle out immediately and never do anything.
Again - i've never done it, either way, but it's well documented.
In Process - Russian Imperial Stout, Nelson Sauvin Rye IPA, Mild No.3
In Kegs - Barley Wine, Apfelwein, Wild BlackBerry Wheat, Coffee Oatmeal Porter
Gone - so many :(