Can I apply for a start-up permit if I currently have highly skilled migrant status in the Netherlands?

Yes, provided all other conditions are met. In principle, if the purpose of your stay changes you can apply for a different, that is new, residence permit. One condition in this regard is that they are supervised by a reliable business mentor (facilitator) in the Netherlands. Some facilitators work on commercial basis (not all), alternative is you go through the self employed person procedure: ind.nl/en/work/pages/self-employed-person.aspx

If you have a highly-skilled migrant (kennismigrant) residence permit and would like to start your own business under the start-up rule you can apply for the start-up residence permit if you fulfil the requirements for the start-up scheme.