To describe my question, I'm going to use example sentences:
The group saw that there was a need to make the necessary revisions to tailor it to each institution before the model could be applied, taking into account their particular size and other conditions.
The group saw that there was a need to make the necessary revisions to tailor it to each institution before the model could be applied, taking into account its particular size and other conditions.
First of all, am I grammatically allowed to say 'their' instead of 'its' when I've said "each institution"? I know that sometimes 'their' is used in the singular sense... but barring this case, would it be grammatically correct/possible to say 'their' when the association is with "each institution"? In other words, I'm unsure if when I've said "each institution" that I'm forced to work with the concept in the singular in latter parts of the sentence, even though it would obviously imply multiple institutions if the grammar associated with the use of "each" is neglected.
Secondly, and this is quite related to the first, I am wondering that if I say 'their', that it is actually referring to multiple institutions (plural) even though this is not explicitly stated the way the sentence is written; by simple deduction in the mind, it can be seen that it would be multiple institutions.
Thirdly, is there something not so right about the way these sentences are written? Particularly with respect to the use of 'particular' and the singular 'size' when there are multiple institutions. I've used the singular basically because each institution has only one size, not many, but could plural also work?