I need to consolidate two web products that have some similarities and many differences in labels and groupings. For round 1 testing, I plan to do open card sorting with content from both sites. I would test product 1 users, product 2 users and internal group with industry standards knowledge. I'm hoping that by triangulating with the 3 groups I will have enough insight to build an IA to test with TreeJack. Is there anything else I can do to accommodate both product users' mental models?
Depending on how many categories your open sort produces you might normalize and consolidate those into a very de-duplicated handful of categories which you can then use in a closed sort. This is a good intermediate step that lets you start to evaluate assumptions (your normalized category names) before you try to validate an entire taxonomy.
In the technology and business context:
In the technological context, product consolidation is important when both systems have a common framework (which also means that maintaining code involves simple replication) it is important to define the skeleton with common elements at the beginning and then, thanks to the final results of segmentation, to diversify the functionality (define differences in IA, based on the existing common core)
in the context of segmentation and research:
it is worth defining the target groups of individual products and based on them design the difference (mental models), depending on the priorities, such elements as category trees may vary. In the initial phase, however, I would minimize the difference just to preserve the common core. Then, however, it gradually introduced differences depending on the preferences of end users and business goals.