Can you create your own MCP to connect to a third-party company's software even if that company doesn't offer one?

No. If a company (the example given was Intuit) doesn't offer an MCP, you cannot build one yourself to connect into their product through Claude — the company itself has to build and offer that MCP. You can only create an MCP for an application that you yourself built. You cannot take a third party's existing application and wrap an MCP around it without their control/approval, since the company still controls what integrates with their platform. Separately, Claude effectively functions like an app store for MCPs, requiring approval before an MCP is listed. To bypass that approval wait, you can build and use a custom connector instead — anyone can then use that MCP through a custom connector without it needing to go through Claude's official approval process. This is what one team did while waiting on Claude's approval.