The opportunity for overstriking counterfeit coins on official ones only rarely arose. Obviously you'd need two denominations of similar size/weight,
Two of the overstrikes I posted above are on larger modules. size and weight are not so important for unofficial coinage, as they are usually smaller than official coins. The series that I collect the most of (unofficial Siscian VLPP's) tend to be at least a millimeter smaller and usually weigh less...most importantly, they have less silver than official VLPP's.
As for opportunity/ reason for unofficial overstrikes, there are a few, and Bastien wrote about this extensively. The period of A.D. 318- 363 was a counterfeiting epidemic, kicked off by several things. The reasons below are from Bastien, though I don't remember if he also wrote about how the IOVI coinage of Licinius (reduced to 12 and a half) was not accepted outside his territory; which is why you can find examples that are overstruck, often with campgates-- see example below, also another coin struck on larger module.
Overstriking seems to occur at the beginning of a coin shortage as a stopgap to introduce the new coin of the realm (or at least a crude facsimile) into circulation. Eventually demand dies down and proper flans can be prepared...at least that is what I imagine happened.
A.D. 318 -330
monetary reform of Constantine--new VLPP have circa 4% silver
circa 335 - between 342 to 348
in 335 A.D., the number of nummi to a pound was raised to 192
A.D. 348
introduction of the maiorina
A.D. 350
usurpation of Magnentius
A.D. 354
after the fall of Magnentius, the maiorinae was replaced by the half maiorinae
Back to the OP coin, I believe it is merely double struck, as I already posted (maybe I shouldn't have mention how it reminded me of overstrikes); but I would say it is unofficial. For coins like this, the burden of proof has to be trying to show it is official, not why it is unofficial. I also don't like the chipmunk cheeks on the OP coin!