It's not practical in a lot of organizations, but something I like to do, when possible, in the face of a non-consensus decision is simply to wait.
That might seem inconceivably frustrating for people who like to make continuous changes - especially if the delay is weeks, months or even years. But sometimes a good idea or answer will develop during that time.
If a good solution doesn't emerge, then sure, it's possible that outside pressure may make it necessary to select one of the options anyway. But I think that's rarer than people expect.
It's best applied in situations where both direction A and direction B lead to significant downsides, I think.
Instead of choosing one of those and getting stuck with (and having to justify) the consequences, wait until the downsides can be reduced, or an option C becomes available.
That might seem inconceivably frustrating for people who like to make continuous changes - especially if the delay is weeks, months or even years. But sometimes a good idea or answer will develop during that time.
If a good solution doesn't emerge, then sure, it's possible that outside pressure may make it necessary to select one of the options anyway. But I think that's rarer than people expect.