The key issue here is the meaning of "possible." Obviously, a monopolist will be able to charge more than a seller in a more competitive economic environment, but that does not mean that a monopolist will be able to raise prices indefinitely, as there are several factors that put downwards pressure on prices.
First, there is a certain price buyers are willing to pay for a given good. For example, if a monopolist cornered the entire market for avocados and started raising prices, many people might choose not to buy avocados. Therefore the monopolist has to set a price that maximizes profit by balancing price per avocado against number of avocados sold. Obviously, a monopolist has a greater advantage in selling necessities such as medical care, electricity, or clean water than selling luxury goods, but still, price per item must always be balanced against total sales.
Next, if a monopolist prices certain goods or services too high, that gives competitors incentives to enter the market and disrupt the monopoly. Where a monopoly is run by the state, that might not be possible, but still people might be incentivized to steal or find alternatives. For example, if a power company has a monopoly on electricity and charges exorbitant prices, people might invest in rooftop solar or illegally tap into the power grid.