You've just downloaded some content from a manufacturer's site and realize that none (or many) of its most interesting parameters are not going to show up in your schedule. This is due to the lack of a common shared dictionary of parameters that we can all rely on. Revit's "system" parameters like Width and Height for some components (like Doors or Windows) just work automatically. Just starting out with a door template means that at least a couple parameters will work without any extra effort. Not true for enough others though.
The Autodesk Family Style Guide (AFSG) while primarily focused on the needs of Autodesk's Seek site also provides a set of shared parameters we can all use (check out ANZRS too). It's weakness is relevance and timeliness. It has a lot of MEP related parameters but doesn't delve into other disciplines seriously and it's really late to the table. Most of the firms that have been using Revit seriously have already dug into their own shared parameters by now. Redoing their library to be in line with Seek and the AFSG doesn't actually begin to help them unless they really start using a lot of Seek content, which is another can of worms.
Rather than continuing to lament the situation this post is intended to provide one solution to getting "foreign" content to work within your existing project(s) and template(s). Assuming you've already mapped out your own shared parameter strategy you just need to connect the dots between the parameters the family is using and those that you wish it was referring to, your own.
It's rather simple really. Add your own Shared Parameter versions of the critical parameters in the family you are working on. For each, in the formula column enter the name of their equivalent parameter. This maps (connects the dots) their parameter value to yours.
Now you can schedule their component along side your own, even tag if necessary. It's a lot simpler than trying to remap all their parameters to your own by replacing them.
It is a little risky in that people will have two places that the values could be touched, their parameter and yours. I usually just segregate them in a separate Group. Just let your teams know how you are dealing with content obtained from other sources and it's not mysterious anymore.