Using single-supply OpAmps with a bipolar-supply OpAmps in the same circuit
If the signal out of the dual-supply op-amps is also bipolar around the virtual ground rail, the single-supply parts will face challenges with such signal - unless clipping at the virtual ground rail is the design intent.

Assuming that all signal in the single-supply op amp portion of the design is definitely above the virtual ground potential, the "new stage" does not use some internal-to-the-chip negative rail, it uses the virtual ground as its most negative supply rail. 

One point of consideration for such designs is to ensure that the virtual ground itself is a very low-impedance rail with sufficient current sourcing and sinking capacity. Use an op-amp based rail splitter with hefty decoupling capacitors between all rails, and perhaps add a BJT stage, to achieve this. 

Alternatively, use a purpose-built rail splitter part such as the Texas Instruments TLE2426 for the virtual ground. 

Also note that your single-supply stage output will be bound between Virtual Ground and the positive rail, not utilizing the lower half of the possible voltage range. In other words, output signal peak to peak is limited to ~4.5 Volts (assuming RRO OpAmps) and not ~9 Volts.