Is it possible to be addicted to more than one substance?

Yes. Known usually as “polysubstance dependence,” addiction to more than one drug is possible, and it is unfortunately becoming more common as access to illegal substances becomes more and more open.
There are typically two instances in which an addiction to more than one drug occurs.
The first typically happens when an individual suffers from a single addiction, receives professional assistance in the form of rehab, and maintains sobriety for a little while, before relapsing with another substance. This could be due to the additional substance’s relative accessibility (compared to the one that they used to abuse), or the individual’s feeling that the additional substance provides more of a high because they have not used it before. In rarer cases, those that suffered from an addiction but also had additional underlying mental health problems that were treated with another medicine could become addicted to that medicine. An example of this would be a cocaine user with ADHD. The user may very well have been treated for the cocaine addiction, but the medication for ADHD may become the new vice they resort to. This, according to experts, is known as cross-addiction. Cross-addiction does not have to just happen with other drugs, either. Individuals can develop  what is known as a process addiction to things like sex, gambling, or even shopping as well.
The second instance in which an individual can become addicted to more than one drug is when they abuse several drugs infrequently enough to not qualify as addiction separately, but frequently enough to qualify as an addiction when combined. An example of this could be an individual that abuses prescription drugs, marijuana, and LSD. They may not meet the criteria for dependence for any of the three by themselves, but they may crave at least one of the three (or a combination of two) frequently enough for it to be assumed that they are addicted to them together.
Treatment for polysubstance dependence is a lot more difficult than it is one for one drug, primarily because each drug that is regularly consumed must be counted for and treated as a separate issue. This means that the detoxification may be longer than it typically would, and that the withdrawal stage could be a little more drawn out, as your body fights to get rid of more than one foreign body. The good news, however, is that no matter the number of addictions you may be suffering from, professional addiction treatment is more than capable of helping you eliminate them!