And as long as you're not doing anything disk-intensive (and definitely most Mathematica operations are not disk-intensive), the performance cost of using a VM is negligible.
Mathematica runs well in a virtual machine-I regularly do so for testing purposes. You can use a program such as Parallels, VMWare Fusion, or (the free) Virtual Box to create a virtual machine running macOS Mojave. One solution that does not involve upgrading Mathematica or downgrading macOS is to use a virtual machine to run Mathematica. Whole sections of the FrontEnd had to be thrown out and rewritten from scratch. We've been working on rewriting the FrontEnd in Cocoa for several years, but it was not a simple or easy project (especially when you have 30-year old Macintosh code, such as QuickDraw, hiding in various places). And, unfortunately, creating a 64-bit 11.3.1 impossible, because the 11.3 FrontEnd is a "Carbon" application, rather than a "Cocoa" application. As already stated elsewhere, versions 11.3 and earlier simply cannot run on Catalina because Apple removed support for 32-bit applications.
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