Complex product variation problem

On the Website that I am currently working on I am entering product information. Some of the products have numerous different variations. I’ve seen other websites that have a bunch of different variations for a T-shirt: Size, Cut, Color, Image. These websites typically don’t use a single drop down menu or use on/off buttons.

One product has the base product (Housing and circuit board) and then has up to 5 other parts installed on it (Sensors installed in slots) and then the option of multiple power supplies. Each of these parts has an individual part number that could be ordered separately. If i use the standard variable part option and enter each of them individually I’d have a total of 6 different attributes. Power supply has 5 options, Slots 1 & 2 has 6 each, and Slots 3-5 has 31 options each. If I made a variation for each option it would total out to around 5 million.

Is there an option, setting, extension, plugin, etc. that would allow me to enter the base unit’s part number and price and then for each of the options they selected add a new part number and increase the price by the individual sensors cost?

Thanks for the help.