You can absolutely do this! this is similar to the process that is used to produce Utopias and other very high alcohol beers.
After primary, I would rack to a secondary fermenter (keep enough headspace just in case) and pitch a healthy started of the second yeast. You may consider adding some yeast nutrients as well (similar to what would be done for a Mead) to promote good yeast health. Let this go for the same amount of time that you would normally let a primary fermentation go (I use 2 weeks as a rule of thumb). Make sure you take gravity readings after you rack so you have a new OG for this second "Primary" fermentation.
Finally I would rack to a secondary (tertiary?) for clearing and bulk aging. I would also be extra careful about oxygen in these racking steps since this will be a beer kept for a long time and there are additional stages that could lead to oxygen based spoilage.