Why create complexity by adding in another type not to mention the costs associated with the development of a 5th gen plane...the most cost effective solution would be to go for either J20 or J31 along with TFX in numbers....
We need to refer back to what the PAF itself is saying ... e.g. (1) the ACM said the PAF is looking "beyond" 5th-gen, (2) they set up AvDI to basically take on the design work of the FGF, and (3) they want to carry out most of the development in Pakistan in order to acquire and fully control the technology in-house. This is basically the markings of an original design, and not the TFX, J-20 or FC-31.
As for "why" they would want it an original design, there are several reasons:
First, this specific program could be meant to replace the JF-17, which would be due for phasing out in the late 2030s and early 2040s. In this respect, the PAF would need a fighter it can induct in numbers.
Second, they want to spend the next 15-20 years to produce a fighter that will be a contemporary of the fighters emerging in the 2030s and 2040s. In other words, stop playing catch-up where after having JF-17, we started seeing the world move ahead with 4.5 and 5th-gen.
Third, going off-the-shelf - even with the FC-31 - might not provide the sufficient amount of technology ownership necessary to build a robust aviation base in Pakistan. The FC-31 or TFX routes might not take PAC very far from where it already is - i.e. maintenance and manufacturing a portion of the sub-assemblies.
Fourth, actually design a fighter that is uniquely tailored for the PAF's requirements, which might emphasize lower operating costs, scalability, customization and future features, such as optionally piloted modules (switching the plane from being manned to unmanned) and controlling a flight of UCAVs.
Regarding cost. Sure, there'll be a savings in development by going for two off-the-shelf designs, but there will also be cost increases in operating so many large twin-engine jets. In this market, there are interestingly no other lighter weight designs optimized for low cost operation and expendability. None.
Another single-engine lightweight jet might seem off-putting, it might remind some of the limitations of the JF-17 all over again. However, the JF-17 was meant to replace F-7s. The alternate way to look at a lightweight 5+ gen fighter is to view it from the angle of future air warfare. A lightweight, low-cost and expendable design can be used as a manned or unmanned aircraft, the latter optimized for very high-risk offensive missions.
Fifth, having an original design with majority technology ownership and development in Pakistan would provide Pakistan with its own exportable good. A program of this nature is something you could offer to many states, and even a few sales would amount to billions in dollars of production and after-sale support work for the economy.