Is there a prohibited region in $P-V$ plane? Polytropic process generalize the particular thermodynamic processes with 
$$P V^{n}= \mathrm{constant}$$
Where, if $n$ changes, the curve on $P-V$ plane changes, as shown in the diagram.

The orange region is not touched by any curve, so there is no value of $n$ for which the gas goes directly in to the orange region.
Why is that? I do not see any particular reason why there should not exist a process to make the gas go into the orange part.
 A: It's simply inherent to the definition of polytropic processes that they don't allow the system to increase both its pressure and volume at the same time. That doesn't mean you can't increase a system's pressure and volume. You just need a non-polytropic process to do so. For example, it could be a compound process consisting of two polytropic processes with different values of $n$, with one being run in reverse - like half of a heat engine cycle.
A: In a polytropic process other than adiabatic, you are controlling the temperature in tandem with P and V in such a way that n is constant.  You can certainly achieve negative values of n by controlling the temperature appropriately.
From the ideal gas law, if T and P are expressed parametrically in terms of V, then:$$\frac{P}{P_0}=\left(\frac{V_0}{V}\right)^n$$
$$\frac{T}{T_0}=\left(\frac{V_0}{V}\right)^{n-1}$$
Just substitute a negative value of n.
A: Assuming there is only one molecular in this box and assuming it is a closed system with initial P-V state is defined. The question becomes: can the system move to anywhere on the PV diagram?
Well we can adjust volume to any number. Then the question becomes: can pressure reaches to any values on PV diagram?
Pressure relates to impacting intensity and frequency. By increasing its kinetic energy or its speed, both intensity and frequency increase. So it seems that we can control pressure using temperature or heating/cooling until the limit of molecular is reached. At this time, you can say there is a prohibited region but not as the orange zone in your plot.  
