As you said, the rules for shoving say:
If you're able to make multiple attacks with the Attack action, this attack replaces one of them.
Since the shove only replaces one of the attacks, you then have enough actions left from the other attacks to shove again. Of course, this assumes that you have enough movement to move 5 feet forward to get into range to shove the creature again.
If you have attack(s) and movement available, then you can absolutely shove multiple times.
This argument is essentially the same one that you can read with regards to grappling in this Q&A.
Jeremy Crawford, lead rules designer for D&D, agrees with this ruling (even including the very similar case of Grappling):
If you take the Attack action and have multiple attacks, you can
replace any of them with a grapple/shove.