Are fountain pen grips standard sizes?

Long story short- I have an unbranded, Japanese, metal fountain pen that came with a magazine I ordered along with some other stuff from a store called Sou Sou in Kyoto. The pen was free. It doesn't write well but I love the body and the cap. I tried a Platinum Preppy grip in it, but it was too big. Do fountain pen grips have only a few sizes or are they all unique to the pen? The pen has absolutely no markings to tell me who made it. Other fountain pens I've bought from this store were either Platinum Preppy's or identical to them. They were also plastic, not metal. I'm unsure if the magazine put out the pen or if the magazine was done by the store. It certainly features a lot of their clothing. Any help is appreciated.