Information about a device's IP addresses of the other type can often be queried, but not using ARP or another protocol that is part of.
For example, in Microsoft Windows:
WMIC /NODE:"192.0.2.1" /OUTPUT:"outwmic.txt" NICCONFIG Get Caption,Description,IPAddress,MACAddress
Obviously you should customize the IPv4 address, and can customize the output file. You can also get more information, like details that will show you the subnet size. Try leaving off everything after the word "Get" to see some more of the columns that you can specify.
I'm sure there are other solutions, including some commercial solutions (e.g., Kaseya is known to exist for Linux). I'm sure some of the available software works on Unix-style platforms. WMI is Microsoft's fancy term for their software that uses WBEM, and SNMP may also be a protocol commonly used (based on warren's Serverfault question: actual or de-facto alternatives to WMI exist for Linux and Unix). The downside is that, although the technical capability does seem feasible enough to exist, differences may cause this to be non-standard enough that you may need to plan to spend a bit of time developing/testing a customized approach.
I presume the ARP cache [...] ?
This didn't look like the main question. I'm briefly mentioning it here so my answer doesn't seem incomplete. See my comment (provided under your question, not under any of the answers) about where I already discussed ARP further.