After a few moments of nothing you get your first lead.
Abjurations to Transmutations, an Arcanist's Almanac

As with many secular Orders the Order of Arcane Artifice is unusually specialized and often called upon. Unlike the Order of Magic Architects, and other noble Orders of that sort, the Order of Arcane Artifice is one of the few often commented on secular Orders that comes from this Prime. They are known for their incredible works in any number of different fields but are the foremost creators of magical transport, items, Trinkets, and other such novelties.

In Righting the Angles, Building the Towers you read;

Without any doubt the most adventure minded of the Order of Magic Architects have political connections with the Order of Arcane Artifice.

In Sights and Attractions of the Realms you find, a small mention of the Order of Arcane Artifice in relation to places they have found over the years.

Finally, Reaching the Transfinite had this to say;

Whilst the Order of Arcane Artifice was founded on our Prime, it has since expanded it's working instruction. Unlike other Orders that are recorded to be on multiple planes this is not just a sharing of knowledge. The Order of Arcane Artifice has a Guildhall in Sigil itself and is one of the few Orders to own a Permit of Permanent Gate. It is even said that when establishing his life's work, the Order, Guildmaster Vaden Justis met with the Lady of Pain herself. This may explain his lack of a left arm in the Prime and Astral plane, as rumor says that the payment was quite high indeed.