Max tire size on road rim
 

I am planning to turn my old faithful do everything touring bike into a tracklocross. I am pretty confident I'll be able to fit 43mm tires into the frame but I'm not sure about the rims I've got.

The wheels I'll be using are the stock wheels off my cinelli Tipo pista so pretty standard 700c fixed/single speed deep aluminium rims. They obviously run 25-28mm normally (think they came with 28) and I've fitted 32mm to similar rims in th past.

So my question is can I achieve the big tires I want with my current rims or am I gonna have to buy different wheels?

TIA

It will be fine.

See the following chart >>> https://www.wtb.com/pages/tire-rim-fit-chart

You should match the tire width to the rim width. So, for a 43mm wide tire, you should use a rim with an inner width between 19mm and 25mm for optimal performance, although you can use a rim with as little as a 17mm inner width. Anything less, and the tire will get a severe lightbulb shape, and roll sideways when cornering.

Besides the rolling issue mentioned by @TejanoTrackie, running wide tires on narrow rims increases hoop stress on the rim sidewalls. The hoop stress increases with tire pressure and can be reduced by running the tires at lower pressure than you ordinarily would use.