I don't think the app will let you start a second order before you've picked up your first order, although I've never specifically tried it.
I once had the app fail to realize I had picked up my order and I was unable to do new orders. I ended up deleting the app and reinstalling it and then I could order again. That was a few years ago, though, and they've changed the app several time since, so maybe I shouldn't assume that an order still awaiting pickup blocks new orders.
Maybe I'll try it next time I want to use points and a deal at the same time and see if you can order while another order is still in progress. If that still isn't allowed, I should probably then try placing the second order on a different device (one on iPhone, one on iPad for instance) to see if the limitation is because an instance of the app can only handle one order or because some account limitation is the problem.
If that doesn't work, two devices logged into different accounts would be the next thing to try--that's got to work. I'm using "Login with Apple" for my McD account. I could make a new McD account using "Login with Google".
