You can handle your individual amplifier stages like black boxes. With opamps, the problem can be the DC component of your signal. If you need to amplify the DC component, you must make sure that after each stage it stays close to zero volts. Temperature drifts can affect it quite a lot. Then the best is to use chopper-type opamps which are stabilized even with a high gain.
If you only need the AC signal component to be amplified, use capacitive coupling between the stages. For high gain like your 80 dB, make sure you use a lowest-noise opemp as the input stage, otherwise the noise will saturate latter stages.
Designing for a high gain looks easy but the real devices are often difficult to behave as desired. Try to gradually make and connect the stages till you have a good and stable amplifier.