The short answer is: yes, especially if cybersecurity is at the forefront of your mind. It's important to understand why from a legal and technical standpoint, which we will discuss further.
What's a router?
A router is a device used to join the same network. Your device, such as a laptop or smartphone, connects to the router and then can access the internet. The router provides a local IP address to the connected device, however, all devices will have the same external IP address provided by your internet service provider (ISP). You can connect to a router with a network cable (ethernet) or wireless (wi-fi). Wi-fi is the ability to connect to the router device through wireless network technology, and has made it easier for people to join the same network.
Now that we covered the basics of how a router works, we can dive a little deeper into the nuances of why sharing an internet connection with another business is probably a bad idea.
Is it legal to share a connection?
It depends on the service contract with your ISP. If the wording in your contract explicitly states sharing, subleasing, etc. with another party is prohibited, you're breaking the contract. Remember: ISPs can determine if there has been unusually high usage which may point to illegal sharing of services. Your provider may monitor your account should they notice a change in usage.
Additionally, if you are a business attempting to use another individual or commercial account to access wi-fi without their knowledge or consent, you could be breaking the law. Depending on what state you live in, joining an open internet connection without permission, wi-fi "squatting" or "mooching" is considered illegal. The Computer Fraud and Abuse Act makes it a felony to knowingly access computers---including routers-- without authorization. Penalties can run anywhere from $5,000 fines to imprisonment.
So let's say your business and another business knowingly decides to split the cost of sharing internet services, it's totally legal in your state, and no where in the terms of service does it state that sharing services is prohibited.
The next question you should be asking is: Can I trust the employees of the other organization?
Sure, you have all the policies and procedures in place so that your employees aren't accessing websites that are forbidden, you have firewalls and antivirus programs in place, but what about the other business? Should an employee at the other organization accidentally download malware, or worse, child pornography, then your business will be at risk. You'll also be sharing your network, which would make it easy for the other organization to hack into your computers and any other devices connected to the network. Additionally, if the other business housed the router at their offices, that means anytime the internet goes down you would have to rely on them to restart the router or call the ISP.
From a technical perspective, it would be possible to put a firewall in place to separate the internal networks should you move forward with sharing a connection with another business. For example, if two businesses were under the same management and happened to be within the same building, from a cost perspective it would make sense, provided you have all the security measures in place.
The negatives outweigh the positives when it comes to sharing a router and/or internet connection, for both individual and commercial use.