I work with someone who thinks that more than two is excessive, but I really believe it depends on your needs. I prefer a large purse with a wristlet inside plus my lunch bag. But that is what fits my personal preference and needs.
Some people like to work out over their lunch break so they might have a gym bag. Others need to carry files and / or a laptop computer back and forth, so they might have a separate bag for that.
The ones I don’t understand are the women who are so proud of their tiny handbag but end up carrying their phone and keys in their hand. What is the point of that tiny bag if you can only carry a lipstick and a pair of Barbie shoes? I have also seen women carrying a purse, a laptop bag, a lunch bag, and an extra tote bag. What on earth is going on in these bag ladies’ lives that they need to carry everything they own?
For a while, I did carry a very large tote that could fit my purse, my lunch bag, and anything else I might need but it just got to be too bulky for me. I downsized to my current arrangement so that on the days I do not take my lunch, I do not have more bag than I need.
Personally, I think two to three is sufficient for most people. If you have to carry a laptop bag anyway, perhaps downside your purse so that it fits inside instead of carrying it separately. If you regularly use the gym at the office, consider leaving some of the items at your desk instead of carrying them back and forth. Keep it simple!