Unless a monopoly is allowed to exist due to a government license or protection from a strong patent, markets have at least a few sellers. When a market has multiple sellers, at least some of which provide a significant portion of sales and recognize (like the monopolist) that their decisions on output volume will have an effect on market price, the arrangement is called an oligopoly.
At the extreme, sellers in an oligopoly could wield as much market power as a monopolist. This occurs in an oligopoly arrangement called a cartel, where the sellers coordinate their activities so well that they behave in effect like divisions of one enterprise, rather than as a competing business, that make independent decisions on quantity and price. (You may be familiar with the term cartel from the OPEC oil exporting group that is frequently described as a cartel. However, though OPEC has considerable market power and influence on prices, there are oil exporters that are not in OPEC, and internally OPEC only sets member targets rather than fully coordinating their operations.)
In theory, a cartel would operate at the same production volume and price as it would if its productive resources were all run by a monopolist. In a cartel, every member firm would sell at the same price and each firm would set its individual production volume such that every firm operates at the same marginal cost.
For the same reason that monopolies are considered harmful, cartels are usually not tolerated by governments for the regions in which those markets operate. Even the collusion that is a necessary component of a true cartel is illegal.
However, although cartels could theoretically function with the same power as a monopolist, if the cartel truly contains multiple members making independent decisions, there is a potential instability that can undo the cartel arrangement. Because monopolists gain added profit by reducing production volume and selling at a price above marginal cost, individual members may see an opportunity to defect, particularly if they can do so without being easily detected. Since the cartel price will be well above their marginal cost, they could profit individually by increasing their own production. Of course, if the defection is discovered and the other members retaliate by increasing their volumes as well, the result could be a substantially lower market price and lower economic profits for all cartel members.
Another problem for cartels is how to divide the profits. Suppose a cartel had two member firms, A and B. Firm A has more efficient facilities than Firm B, so the cartel solution will be to allow Firm A to provide the bulk of the production volume. However, if Firm A claims its share of the profits should be proportional to its share of the production volume, Firm B may object to voluntarily withholding its production only to allow to Firm A to grab most of the sales and profit, and the arrangement could end.
Also, since optimal cartel operation means that all firms set production so all have the same marginal cost, the firms need to share internal information for the cartel to determine the total volume where marginal revenue equals marginal cost and how that volume gets divided between firms. Again, some firms may have the incentive to keep the details of their operations private from other firms in the cartel.