I agree with Charles, but I set up our system to ask for more because (a) it helps you get a better picture of the supplier and (b) whilst GFSI may be enough to satisfy clause 3.5.1.2, you're almost certainly going to need more information to risk-assess the raw materials as per 3.5.1.1.
Alas it is also the case that GFSI doesn't always correlate with a good standard of general operation... 
Thanks to all for your help.
Regarding the Raw Material Risk Assessment i thought to manage the question considering only the intrinsic risk of the single ingredient independently from the system of the supplier.
Schematically I think in this way (searching to simplify the job):
- Supplier is enough safe? YES --> I can buy from him; NO --> I cannot buy from him
- What is the risk of a determinate Raw Material --> It depend only from the single raw material (e.g. dried pulses can have allergens and foreign body problems - oregano can have pesticide and vulnerability problems - ecc.) --> So I require risk mitigation measures based on the single raw material. (e.g. I can ask allergen analysis to a dried pulses supplier on every batch that I buy, or the supplier have to convince me that It have the risk under control with some documentation or other).
Otherwise I don't see any other chance to auditing every supplier and assign subsequently the grade of risk of every single supply.
I would be grateful for every consideration/correction
Regards