A classic example, related to the point made by @GuyLouzon, is access pricing in network industries.
A telephone network is a natural monopoly. The modern approach to regulating this market is to force the monopolist owner of the network infrastructure to allow competing telecomms services firms to buy access to the network. This allows those rivals to offer competing retail telephone services using the monopolist's infrastructure rather than having to build their own.
The price that the incumbent charges firms for network access is regulated. Ensuring that monopolist does not set the network access price too high means that downstream firms can profitably buy access and thereby enter the market for retail telecommunications services. While the fundamental natural monopoly problem has not gone away, regulating the access price at least helps to ensure the retail telehone service market is not also monopolised.
If you would like to read more about this example, I'd recommend "Competition in Telecommunications" by Laffont & Tirole.
One can easily build a model of this situation. Suppose that retail telephone firms earn profit $\pi_n$ when there are $n$ firms in the market. Make the standard assumption that $n\pi_n\leq m\pi_m$ whenever $n>m$ (industry profit is lower when there is more competition).
The wholesale firm sets a price, $p$, for access to its network. Firms will choose to buy access so long as $\pi_n>p$. The highest price the monopolist can charge if it wants to serve $n$ firms is therefore $\pi_n$. Thus, the monopolist can serve one firm and earn profit $\pi_1$, serve two firms and earn profit $2\pi_2$, serve 3 firms and earn $3\pi_3$, etc. Because $n\pi_n$ is decreasing in $n$, the monopolist optimally sets $p=\pi_1$ and grants access to a single firm, inducing a downstream monopoly.
A policy that constrains $p<\pi_2$ would, on the other hand, induce more than one firm to enter downstream and thus result in more downstream competition than when the price cap is not in place.