Contrary to popular belief, HP wasn't the only Itanium vendor in town. This is an incomplete list, especially considering the numerous E8870 rebadges that went around - but it might be interesting from a historical perspective.
The big one. Three distinct generations of custom chipsets, and probably the destination of well over 90% of cumulative Itanium volume. Systems went up to 64 sockets during the Montecito generation, and to 32 sockets in the Tukwila/Poulson generation. (A 64-socket Superdome 2 was announced but not, as far as I know, shipped.)
The Xeon-based Superdome X family is a Superdome 2 with Xeon cells instead of Itanium; later Superdomes use SGI technology and are not part of the Integrity lineage.
Probably the second highest-volume vendor in the North American market. Sold very large (into the thousands of sockets) Itanium shared-memory supercomputers with a custom interconnect - the Altix 3xx/3xxx and the Altix 450/4700. Altix4 was replaced with Altix UV, a Nehalem-EX system; Itanium UV configurations were roadmapped and may have existed internally, but never shipped (presumably due to low demand for Tukwila-based systems.)
Sold some systems under the ES7000 brand, largely for Windows Server users. Explored using Itanium platforms as the long-term emulation host for its OS 2200 and MCP mainframe customers; OS 2200 may have been emulated internally on IPF but never, to my knowledge, shipped. As a footnote, Unisys mainframes with custom CISC CPUs used the Itanium2 bus and parts of its system infrastructure, likely for the sake of design reuse from the ES7000 family.
Sold large scale-up IPF systems into the European market as the Novascale family. Also sold Itanium systems running GCOS 7 (V7000, under Windows) and GCOS 8 (V9000, under Bull's Helios Linux) to their legacy mainframe base. Later Novascale GCOS systems - starting with the Tukwila family - were rebadged Intel Crater Lake SDVs.
Developed a custom chipset for up to 8-socket systems during the Montecito generation. Mostly exited the IPF market afterward, though continued to sell rebadged HP Integrity systems as the HA8500 until approximately 2020 to its domestic base.
Montecito-generation Intel reference platforms use a Hitachi chipset due to the cancellation of the Bayshore chipset.
Had a large family of IPF systems with custom chipsets, the PRIMEQUEST family. Ran Windows, Linux, and Fujitsu's XSP mainframe operating system (under emulation.) Exited after Montecito/Montvale generation; modern PRIMEQUEST is mission-critical x86.
Rebadged HP/HPE systems into the late 2010s as the OKITAC 9000.
Rebadged HP/HPE systems into the late 2010s as the MELCOM ME S.
IBM sold medium-sized IPF systems using Sequent interconnect IP until shortly before the Montecito generation. It was a fairly half-hearted effort, especially after the cancellation of the AIX port.
Carried out significant IPF efforts both internally and via a close alliance with HP. Itanium Express5800 systems were mostly oriented to the Windows market, while the nx7700i systems were a mix of rebadged HP/HPE systems and custom NEC machines, all running HP-UX. Late-generation nx7700i's include configurations unique to NEC, some of which use a custom chipset. This is definitely weird, since custom chipset development is expensive and NEC's 2010s-era Itanium volumes were fairly small and effectively domestic-only, but it may have been a move to preserve inhouse design capabilities.
Also had i-PX9000, Itanium systems running ACOS-4 under emulation. Replaced circa 2011 by the i-PX9800 using NEC custom CISC processors.
For completely unfathomable reasons, Inspur built a 32-socket system to serve as a PRC domestic mainframe... in 2011, running Linux. It later got refreshed with Poulson. Huawei almost did something equally weird, but apparently realized at the last moment that it was a bad idea.