Agree with Fluffagrams that an add-on cage could create territorial behaviour. The mini duna is a bit small for a pair. Something like the standard duna multy could be a good upgrade - you could put the base of the mini duna inside it initially, set up as it is now, and add extra substrate around it with new things to explore out to (if that makes sense). It would make the transition easier/keep some familiarity. Then when they are settled in after a few weeks, take the mini duna base out and just put the contents back in the same place, keeping the old substrate.
A cage change could cause them to fall out, but might not. If it does you still have the mini duna to put one of them back into.
Did you have a new cage in mind? Some people like to go very large and set up quite a habitat (eg a detolf/tank which can then be split into two separate tank areas if they need separating). Others find it depends on the hamster as to whether they prefer more or less space.
Generally though, two of everything is recommended for a pair - eg two houses, two wheels, two water bottles, to avoid them getting territorial over things - but they might still share some things as well. And it could be difficult to fit two of everything into a mini duna. A standard duna multy isn't too great an upgrade but gives a good amount of space, and it's not too expensive (about £33 from Porton Aquapet).
Cage Duna Multy
There is also a maxi duna multy which would give a lot of space for enrichment and depth of substrate for digging tunnels and burrowing, but it would need setting up so there isn't too much open space. It's more expensive but with the maxi duna multy you aren't likely to want to upgrade again. The old RSPCA recommendation used to be 70cm by 40cm continuous floorspace (standard duna multy size) for one dwarf hamster and 80cm by 50cm continuous floorspace size for a pair of dwarf hamsters. So technically the standard duna multy could be a bit on the small side for a pair. The maxi duna would be plenty big enough and give scope for large items like cork logs to add to the enrichment.
There are also bins to make bin cages that are about 80cm by 50cm or between the two larger duna tank sizes. Depending on whether you're up for making a bin cage!
This is the maxi duna multy
Cage Maxi Duna Multy
A detolf costs about £40 but needs two lids making out of wood and mesh, and ideally something to stand it on (some people use Ikea lack tables or kallax units for storage). Here's an example of detolf set ups.
https://www.google.co.uk/search?q=ha...msters&imgrc=_
On the fourth row down, second photo from the left is one that has been divided into two (possibly to separate a pair).
There are quite a few cages that are 80cm by 50cm but not many with small bar spacing - and if they are used to a tank style of cage they may settle better into another tank style (similar environment), but that's just my opinion!
The main thing, if you move them, is to keep familiar smells and layout. So keep all the old substrate and transfer it across (on top of new substrate as you'll need extra for a bigger tank/cage). And try and keep house/wheel/toy layout the same or similar. And no platforms or levels (also encourage territorial behaviour) and I believe tubes are avoided for similar reasons - unless it's a tube/tunnel big enough for them both to fit in so one doesn't claim it and guard it! The cork logs have quite large interiors and some bendy stick bridges do as well.