I was under the impression that most 36v controllers would handle 48v...
Handle, electrically, very likely. But you'd have to check the ratings for all the parts that are connected across the battery bus to be sure of that.
However, there are two things in controllers that may make them not work outside their labelled range, either at all, or for a user's specific needs:
HVC (high voltage cutoff), and LVC (low voltage cutoff), which are used to tell the controller to change it's behavior when the battery is above or below these limits.
LVC is used to tell the controller to shutdown assist when the battery drops below this point, to protect the battery from overdischarge. The BMS in the battery, if it has one, will also have an LVC for this purpose, but it is at a lower voltage that takes the cells much closer to their actual limits, and is harder on them to discharge them to frequently, so the BMS LVC is intended as an emergency shutoff, not an everyday one. The controller LVC is intended for that.
So if you have a controller meant for 36v, it's LVC will be far too low for a 48v battery, and if that 48v battery either has no BMS, or it's BMS fails, there is nothing to stop discharge until it is realy really dead. Since most ebike batteries are not made of matched cells, some of them are going to be lower than others, and may be much lower in aged batteries, or low-quality ones (even when new), and may be overdischarged or even reversed, which creates a fire risk.
HVC can be (but is not always) used to tell the controller not to operate the assist if it's above this limit. If a controller with this is used on a higher voltage battery, it won't operate until the battery is discharged (manually) below the HVC.
It can also be used to tell it not to engage regen braking if it's above the limit, so it doens't damage the battery by overcharging it (because a battery with a separate-port BMS (vs common port) can't stop charging thru the discharge port (regen), no matter how charged or overcharged the cells might be. If a controller with this is used on a higher voltage battery, regen braking won't work, at least not until the battery is discharged far enough to be below this.
There's at least one other thing the HVC could affect but JellyBeanThePerfectlyNormalSchmoo has derailed my train of thought so I'll have to come back to this if I remember it later.