Normally it is with adding any extra low acid ingredients, such as peppers, onions, etc. Also, eliminating any acid called for in a recipe changes it. The recipes are based on ph levels and density basically. That is why there are no safe methods of canning dairy products either. There will be a chart in the Blue Book that gives ph or acid levels for basic foods one would use in canning. But, as you see, if you add extra onions to spaghetti sauce, for instance, you have immediately changed the ph level. The processing times are based on each individual recipes ph level and density. Also, there is no safe method for canning foods, such as gravies and soups with flour or any other thickenings added. Before I knew better, I tried canning some lentil soup that had been thickened. Oh boy, what an awful mess of bacteria I grew!
Usually with fruits you can be pretty safe, as long as that is all you are putting in the jars. Then you process for the fruit that takes the longest canning time. Extra dried herbs can be added to most pressure canned foods, although, as I mentioned, sometimes they do turn bitter.
I was so amazed at just how scientific this all was until I began studying it. Sure opened my eyes. I am so fascinated by it all.