I own three knives right now, and want to buy a fourth very soon.
I've only been a "knife nut" for about 10 years, which makes me a newbie compared to many of the people on this site, but I have owned several hundred knives in that time. I had a period of about 5 years where nearly 100% of my disposable income went into collecting knives. I've owned 4 Striders, 2 Busses, 1 Sebenza, 1 William Henry, an Al Mar SERE, over a dozen Bob Dozier fixed blades, a few custom folders such as a John W. Smith and Emerson, dozens of Spydercos, Benchmades, Kershaws, and 1-2 examples of several other major brands. I never owned more than a couple dozen knives at once; I would sell off my least favorite knives to buy new ones and that cycle would continue. As my tastes changed, so did my collection. For example, at one point I sold off most of my tactical folder (G10, titanium framelocks etc...) and spent a couple years collecting Bob Dozier fixed blades.
Over time my OCD for collecting waned, and I started selling off all of the knives I didn't use or carry. I knew there were people out there that would get more use out of most of my knives, which just sat in a drawer, than I was. I sold many of them through Blade Forums, so I know they went to good homes
After trying nearly every type of folder I could afford, I really fell in love with the Axis lock. I love fixed blades in theory, but I rarely carry or use them and never really need them. I honestly don't "miss" any of the knives I sold. If I didn't carry it on a daily or semi-daily basis, then there is nothing to "miss" by selling it.
I currently own a Griptilian, a 710, and a Contego. The knife I want to buy very soon is an Adamas. With those 4 knives, I think I will be satisfied for many years. I prefer to have a small stable of knives that I really use, carry, pay attention to, and keep in perfect working condition (sharp, lubed, dialed in etc...) rather than having a lot of awesome knives in a drawer. I rotate those 3 knives depending on my mood; they all get used at work and they all get carried as EDC. If I lost any of the three I have now, I would miss them.
There is absolutely nothing wrong with owning dozens or hundreds of knives at once; I'm just happy with 3-4 right now.
I know the thread said "one or two", but as knife nuts go, 3-4 is practically the same (league) as 1-2. I'd be happy with nothing but a 710, honestly. The "OCD collector" in me just focuses on other things now. Maybe I'll get really heavy into knife collecting again one day.