constructing mechanical chase
Ok now we know the want is for the chase to be a verticle space with 2 or more vents and some electrical. Yes this can be done, enclosed vents are required to be triple walled pipe in my state and the wiring must be rated for the temp in that area. Many wire types are rated for 90deg C this is very hot and with some venting in the chase it will stay well below this threshold. The dryer vent may need a booster fan and can be single wall, I always suggest a booster when going verticle or more than ~15' horizontal.