Without 3rd party Software The Answer is NO.
The Program Compatibility have all legacy Microsoft OS Options Supported by your current Operating System, and for the Legacy System it haves WoW(Windows on Windows) for x86 and 16-bit Software.
Compatibility can't cross Platforms for Example:
Windows > Unix Windows > OSX Windows > Linux That happen because the software is compiled to be executed by a diferent Kernel who works quite diferent.
With 3rd Party Software The Answer is Yes partially But not in the way as you are waiting for.
Some developers have made the way to execute programs compiled to be used in another plattform.
In Linux we haves WINE
Wine (originally an acronym for "Wine Is Not an Emulator") is a compatibility layer capable of running Windows applications on several POSIX-compliant operating systems, such as Linux, Mac OSX, & BSD. Instead of simulating internal Windows logic like a virtual machine or emulator, Wine translates Windows API calls into POSIX calls on-the-fly, eliminating the performance and memory penalties of other methods and allowing you to cleanly integrate Windows applications into your desktop.
Wine began in 1993 under the initial coordination of Bob Amstadt as a way to support running Windows 3.1 programs on Linux. Very early on, leadership over Wine's development passed to Alexandre Julliard, who has managed the project ever since. Over the years, as the Windows API and applications have evolved to take advantage of new hardware and software, Wine has adapted to support new features, all while being ported to other OSes, becoming more stable, and providing a better user-experience.
An ambitious project by definition, work on Wine would steadily continue for 15 years before the program finally reached v1.0, the first stable release, in 2008. Several releases later, Wine is still under active development today, and although there is more work to be done, millions of people are estimated to use Wine to run their Windows software on the OS of their choice.
In Windows we have Cygwin
Cygwin is:
a large collection of GNU and Open Source tools which provide functionality similar to a Linux distribution on Windows.
a DLL (cygwin1.dll) which provides substantial POSIX API functionality.
Anyway that 3rd party programs can't handle all software.
And remember Compatibility is Only For Legacy Products you cant have compatibility to a Highter S.O you can do a Workaround to make the software works, or maybe get a patch but not compabitibity as well.