Can I purchase a computer with a partial payment on my card and the rest another form of payment

Yes. Excerpted from Payments & Pricing - Shopping Help - Apple:

Using more than one payment method

You can also combine payment methods to pay for your purchase. ...

Credit card(s) - up to two

As far as I know yes, however we are all end users just like you and are not privy to everything Apple. I would recommend contacting Apple's online store and asking that question assuming that is how you intend to purchase. If you are going to buy from a physical Apple Store you need to go there and ask.

Perfect, thanks John!