During QuakeCon 2015 Bethesda revealed that players will have 12 companions on their journey in Fallout 4. What that journey is, we aren't quite sure — Bethesda has yet to share that, but they have shared player limitations when it comes to romance.
There aren't any.
Well, there aren't any limits with your companions (Dogmeat, Mr. Handy, Preston Garvey, and ‘Piper’ — a newly-revealed companion) – you can romance your companions regardless of their gender. It seems as though BioWare has taken a page from Mass Effect and Dragon Age's book when it comes to romance and love. In Mass Effect, it didn't even matter if the individual you were romancing was human, alien races were cool too. BioWare won't limit your love (within the limits that they give you to love – but feel free to flirt with inanimate in-game objects all you want).
Mr.Handy is a robot, by the way, it's unclear if you can romance robots… But we can hope, right?