The 30-year-old singer welcomed a son named Rex with Joe 10 months ago, and the pair - who have three children from previous relationships, as Stacey has sons Zachary, 12, and Leighton, seven, and Joe has son Harry, also 12 - are already planning on expanding their brood once again.
Joe said: ''Yes, we would love to have another baby. We have really lucked out, we've got four amazing kids and if we have the chance I think we would love another one day.''
The 38-year-old actor insists his partner - whom he began dating in 2015 - isn't rushed off her feet as a mother of three sons and a step-son, as the family always make sure she has plenty of ''girl time''.
But amid the ongoing coronavirus pandemic, Joe is sure Stacey misses having her mother and sister around.
He added: ''Stacey doesn't miss girl time. She's our queen and we look after her. But I'm sure she would love to have her mum around; she really misses her mum who's at her sister's at the moment and in isolation. Her mum comes and spends a lot of time here usually so I'm sure she's missing her mum.''
The couple have found self-isolating during the current health crisis - which has caused schools to close - to be difficult with four youngsters in the house, but Joe says they're starting to settle into a new routine.
Speaking to MailOnline, he said: ''We're doing alright, obviously in the beginning we struggled and we didn't quite know what we were doing and couldn't handle it but we've worked our way through it and got our heads round it.
''When the kids go back to school it's like I'm going to be a free man again - free and single.
''Our kids have got a schedule so they work for a couple of hours in the morning, it's not easy but it's so important. The last thing we need is for a whole generation to fall behind.
''As parents me and Stacey feel it's such a heavy responsibility to have on your shoulders.''
Since returning to his musical ventures in 2013, the former Reuben vocalist has become a valuable member of the British alt-rock scene.
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