There isn't really a 'production line' for PAAMS, per se.
PAAMS itself is just an AAW system, best described as a weapon control system that then fits into a chosen CMS suite. On the Horizon-class destroyers, that was SADOC 3 for the Italians, and for the French I believe the CMS used was called SEIS? And then CMS-1 for the Type 45's.
With that being said, as a software, the original PAAMS on the ten Horizon/T45 DDGs is 'relatively' outdated (in a very loose sense of the word - still a very capable system, but dated), and I would expect any new dedicated AAW ship to be fitted with PAAMS-NG, which is the newer system intended to take advantage of upcoming munitions (initially Aster 30 B1NT, but then also leaving growth room open for other effectors like the prospective 'Aquila') and sensors. It is expected to go to sea for the first time in 2027, when the first Horizon-class DDG to undergo their upcoming MLU - Andrea Doria (D 553) does her post-refit trials and is re-delivered to the Marina Militare. It will also to equip the upcoming Italian destroyers under the DDX program.
There is also a question of what scale of AAW capability you're shopping for. PAAMS is meant to be a full area AAW system for destroyers that have to provide fleet air defense, and hence has been installed only on ships performing that role. The more common capability among frigates is the reduced-scale SAAM (Surface-to-Air Anti-Missile) - which is meant for a self-defense and local air defense capability for frigates and carriers using Aster 15, though the FREDA (Air defense variant FREMM for the MN) run a variant that is a bit more capable to take advantage of their ability to employ Aster 30. The Italians also have a variant known as SAAM-ESD (Extended Self Defence) that they had developed for their frigates, which were designed with a more powerful radar suite than their French counterparts in order to better employ Aster 30 in an escort role. It exists in both the original variant for SADOC 3 and an improved variant (SAAM-ESD++) for SADOC 4 employed by the PPA (and to be employed by the FREMM-EVO).
Given the medium-range capability of the Iver Huitfeldt's the Type 31 would be replacing, depending on what the Danish Navy is looking for either SAAM-ESD or PAAMS-NG could apply. In any case, either variant is certainly applicable depending on the sensor suite they opt for. Compared to their existing design, it would really just be a case of opting for a suitable replacement for APAR Block 1 to datalink with Aster 15/30, as they could easily just replace the SMART-L with the newer SMART-L MM/N (which is effectively what the Horizon program does - S-1850M is being replaced by SMART-L MM/N), if they still want something with that capability. The difficulty would primarily arise in whether or not there is an issue integrating SAAM-ESD/PAAMS within their preferred CMS, and if they have a preferred CMS to work with in the first place (presently they have standardized on Terma's C-Flex).
