Allowable costs and fees for FFRDCs

Trying to get some information on the use of an FFRDC. I received a FFP quote from an FFRDC that included a list of materials. The costs for the materials was extended out and then inflated with a 14.25% markup. We hold commercial companies to a very small fee for purchasing. I have very little experience with FFRDCs and I'd like to know if anyone out there has ever come across this type situation.

The FAR at 35.017-1(d)(2) states: "The sponsoring agreement or sponsoring agencies? policies and procedures may also contain, as appropriate, other provisions, such as identification of?

(2) Considerations which will affect negotiation of fees where payment of fees is determined by the sponsor(s) to be appropriate.

My interpretation is that sponsors who write these agreements should be including rates. If the agreement states the FFRDC may accept work from a non-sponsor (another government agency), then the FFRDC would be submitting quotes/proposals that honor the agreement with the sponsor. If true, shouldn't the other government agency be allowed to review the agreement between the sponsor and the FFRDC.

Am I going in the right direction here or am I out in left field?

Any feedback would be great!