Increasing open loop gain of opamp by chaining
Yes - you can combine two opamps with the aim to improve the overall peformance (not only for enlarging the open-loop gain). HOWEVER, as outlined by Andy_aka you must NOT simply combine two "naked" opamps. 

Instead, the second one must be equipped with an internal negative feedback (reducing gain). In each case, one of the opamp must be inverting and the other one non-inverting (stability against self-excitement). 

Such a combination is called "composite amplifier" (googling for this key word gives you several alternatives). For example, such a combination can be used to combine excellent input specifications of one opamp (noise, offset, input impedance) with good output specifications (output impedance, slew rate) of another opamp. At the same time, the closed-loop bandwidth will be considerably enlarged. Hence, dc as well as ac characteristics can be inproved simultaneously.     

Here is an example, where the excellent slew rate properties of a current-feedback amplifier are combined with the good input specs of a voltage-opamp.







simulate this circuit &ndash; Schematic created using CircuitLab