I've got a character that just picked up the guard dog droid from Keeping the Peace and I'm wondering if it's possible to modify them at all? Add armour, change weapons, enhance sensors/stealth, things like that.

I'd use the rules in Special Modifications and utilize them in some fashion.

Well, you could always give them six pieces of cybernetics, couldn't you?: Adding to characteristics, armour and whatnot. And, if I remeber correctly, according to their species description, a droid can have equipment up to their encumbrance allowance installed instead of carrying it externally.

But is it possible at the start of construction to give them 2 directives instead of 1...Example, Navigation & Repair??

And do you have to start w/ those stats or can you change a couple pre-fab?? give the Astromech droid 2 Agl instead of 1 & 1 on Willpower or something else instead of the 2 it has??

Rules say work with the GM on creating custom options. So it's one directive but that could be unique.

You can add to stats with crafting dice results.