I don't think that the Bodleian actually claim to have the whole collection of the Harkness ballads, although they certainly have a large selection. There are some gaps in the numbered series among the Bodleian's collection (though its possible that not all of the numbers were actually published in the first place). Some of the sheets are not numbered, although they might still be part of the series.

However the Preston Harris Library say only that they possess "many" of the broadsides printed by Harkness; while the Madden collection claims to hold "the almost complete numbered series of the Preston printer, Harkness".

In short I don't know if any single institution holds all of Harkness's output.

If you are cataloguing Harkness I'd love to see more of his version of Barbara Allen which apparently begins "In Liverpool town, where I was born...".