Yes, if the defined work can stand on its own and the unknown addition is scoped separately. You can start the work you understand without treating every new idea as part of the same agreement.
That came up while I was advising on a proposed engagement. There was an original proposal, plus a partnership program that needed more definition. My suggestion was to keep the original work moving and use a separate diagnostic to figure out the new piece.
The useful starting point was being willing to say, “I don't know enough about the business to tell you what you need.”
That is a reasonable thing for an experienced operator to say before investigating. You don't need a confident answer built on information they haven't collected.
Separate the conversation into two parts.
First, what is already clear? Write down the outcome, the work this person will own, and what your team needs to provide. If that work can stand on its own, the new question doesn't necessarily need to hold it up.
Second, what needs to be learned before anyone promises to deliver the additional work? Give the diagnostic a specific purpose. At the end, you should understand what needs doing, what resources it would take, and whether this person is the right one to do it.
That last question was part of my advice too. If another person is needed, the operator can help you figure that out. Hiring someone for one useful piece of work doesn't establish that they're the best person for every problem you uncover.
Be clear about the diagnostic's cost and time commitment. In the situation I was reviewing, I suggested including it without an additional charge. That was a proposed term for that engagement, not a rule that discovery should always be free.
This gives you a practical way to start small with a fractional leader. You can get experienced help on the work you understand while getting better information about the work you don't.
The boundary matters: starting the original engagement should not silently become approval for every new project. Scope the additional work, decide whether it makes sense, and agree on it separately.