There are two answers to this question. The short answer is that there is no limit to the number of shares one entity may own in a specific company. The long answer is a bit more complicated, as certain rules, conditions and restrictions may prevent or discourage large investors from purchasing as many shares as they wish.
For starters, if an investor is looking to purchase a significant number of shares in a company, that investor may be limited to the current market supply. Purchasers cannot buy more than the volume being offered for sale.
Volume aside, the investor may find some regulatory rules discouraging when purchasing large interests in a company. For instance, the investor may be forced to publicly announce the intention to purchase a significant amount of shares and whether he or she plans to take over the company. In this situation, the investor may be required to submit a tender offer for the desired amount of shares.