Square shares will thrive as the company expands to new markets and builds upon its core payments offering, according to Credit Suisse.

The firm raised its rating on Square's shares to outperform from neutral, citing the increasing breadth of its product offerings for merchants.

"SQ’s evolution from a payment company to a differentiated consumer and merchant services platform increases our conviction that the company can extend its business well beyond micro-merchants to include SMB and middle-market companies," analyst Paul Condra said in a note to clients Thursday entitled "The World Is Square." “SQ’s growing product eco-system is increasing its ability to penetrate larger merchants, expanding its payment opportunity while adding incremental subscription and service revenue opportunities.”

The company's shares rose 2.97 percent in Thursday’s session after the report.

Condra noted the company has added point of sale software offerings for restaurants, hardware products, customer relationship management, analytics and payroll software on top of its payments solution.

He estimates Square only has 3 to 4 percent market share of the $2 trillion in payment volume generated by global small- to medium-sized businesses.

“We view the core payment opportunity as very large,” he said. “We believe crypto currencies are not going away and expect that over time they are likely to find more applicable use cases. While this is a small opportunity currently, we view SQ as among a handful of companies - and the only public one – at the forefront of shaping the evolution of this industry.”

The analyst raised his price target to $81 from $44 for Square shares, representing 19 percent upside to Wednesday’s close.

Square shares are up 97 percent so far this year through Wednesday versus the S&P 500’s 5 percent gain.

— CNBC's contributed to this story.