You can have extinguishers other than an F class but they will not touch a fat fire - they tried CO2 and Foam at Heathrow Terminal 1 and it burnt down and at South Mimms Service area & it burnt down, fire blankets were tried at a shopping centre I have had dealings with and it only didn't burn down thanks to a 30 kilo fixed BC Powder system.
If you want to provide fire fighting equipment suited to the risks and if you are interested in property protection and you have fat fryers of over 3litres &/or 300mm dia then you need Wet Chemical - its the only agent, which is why you will not find the F class pictogram on any other type of extinguisher.
One insurer (name escapes me) now makes them a mandatory requirement of providing fire insurance to premises with fryers.
I've watched practical tests of all the different agents and they don't really work, it mainly centre around the temperature of burning fat compared to other liquids (300-400 C as opose to 90)