You might also post this in the trees forum.

Any idea why you think a persian mulberry would be more successful? I suspect they are not getting enough sun.

I do not think that the Persian Mulberry will be more successful but everybody seems to think they are the most tastiest Mulberry of them all . LOL .. (I actually never tasted one!)

By the way, most of them are not getting enough sun but two of them (get at least 8-10 hours off full sun .. but they don't grow enough (possible reason could be (1) I don't feed properly (2) Do not have the right type pollinators (3) Male species(?)

So, I was thinking I could graft the well known type (and since I have couple of them available to take cutting from) and see if that gives me better result. Since last year, I started to feed this plant I was considering as rootstock

Have you ever figured out what species of mulberry yours are? If the leaves are smooth and slightly glossy then you probably have the non-native white mulberry which does not have good flavor.

If the leaves are rough feeling then you probably have the native red mulberry. The red mulberry does have different male/female flowers - sometimes on the same tree and sometimes not.

Have you ever observed that yours produced flowers? If they don't make flowers then they may not have enough sun or may not be mature enough. Fertilizing is generally not an issue. If they make flowers but no fruit then you have a pollination issue.

Squirrels do love mulberries, as do the birds. But esh makes a good point - some mulberry trees are 'male', some are 'female'; you'll see 'blossoms' on the males that look a lot like young berries, but they don't develop.
Even mulberries growing in dense shade will produce some fruit - but not many.

I graft mulberries all the time, using seedlings as rootstock for superior fruiting varieties. A simple bark(veneer)graft works best in my hands, but I have done cleft grafts(they're ugly, but they work.) Dormant-collected scionwood held under refrigeration, grafted onto rootstocks soon after they begin leafing out.

All those Wild Mulberry in the backyard do flower (long flower like typical Mulberry) but never fruit a single mulberry. The leaves are rough and have different shape (perfect heart shape to tooth shape or finger shape) :) ... and yes, the leaf does have rough texture.