Their talismanic striker Jordan Hulme is staying put after a contract was signed for next season.
Hulme scored 20 goals as the team reached the play-offs and Alty have announced the forward has now committed.
It comes after Parkinson and assistant Neil Sorvel confirmed they are staying until 2022.
Parkinson said: “We came so close to a second successive promotion in this our first season back in the Vanarama National League North, and we are hungry to go one better this time round.
“But we want to go one step further and establish ourselves in the National League over the course of this contract.
“The board has shown their ambition and we will work together on and off the field to keep moving this club forward.”
Chairman Grahame Rowley said: “The next 12 months are perhaps the most important in the club’s history.
“We have shown that we can be a big team at this level, and we have major plans to deliver changes that will ensure we are ready for the National Division when the time comes.”