"The first one, absolutely. They frequently do so, even. Most Artefacts prefer not to move on to a new partner until after their previous one has died, and will accordingly refuse to bond to someone new until then if it is attempted. They're more likely to accept people their late partners were close to - spouses, lovers, children, friends. Aside from that, bonding involves a brief exchange of mana, which allows the Artefact to asses their new partner's personality before bonding, and vice versa. If they don't like you, they won't bond.
"As for sharing Artefacts, well, I have heard of it happening. If two people have an exceptionally close bond, an Artefact might agree to working with each one. Two Artefacts will roughly never agree to bonding with the same person, however - and they can tell if there is or was another bond, they leave remnants."