Maybe you can look up a small independent shelving unit that can sit on the floor so they're not stacked on top of each other but still is compact.
On a very quick search there is the following. They may not work for you specifically but could give you an idea...
https://www.amazon.com/Atlantic-Gaming-Not-Machine-Specific-630490063057006304300/dp/B003GB15EK
Or https://www.amazon.com/Seville-Classics-Expandable-Kitchen-Counter/dp/B002ZNJHZE