I figured it out using Cpanel and WHM. Here are the steps for anyone that wants to try it.
1) Create a subdomain in Cpanel for whichever subdomain is being used by WPMU, for example if your new site in WPMU is 1.aaa.com, create that exact subdomain in cpanel.
2) Redirect/Point (while using the subdomain creation function) that newly created subdomain to the whichever alternate subdomain you desire, for this example, 1.bbb.com.
3) Park 1.bbb.com (do not create the subdomain in the subdomain function of cpanel), park only.
4) Create a CNAME record for 1.aaa.com and also point it to 1.bbb.com. (If 1.aaa.com has an “A” record, delete it.)
That’s it!
Cheers!