Theoretically it is possible to run both, but I wouldn't if I were you. This is mostly due to performance issues. Unlike its home products, Symantec Endpoint protection is very light, less than 50 mb in my tests. However, Emsisoft products are generally heavy, taking up some 300mb on my test systems. Enabling memory optimisation in emsisoft can decrease the amount of memory used drastically to less than 50mb, however, you have to note that in this mode emsisoft takes longer to load its virus definitions which I do not advice.
Choosing which AV to install would depend on whether your Symantec Endpoint Protection was well configured. If your symantec endpoint protection is managed by your company, with all the system hardening policies, firewall policies in place, I would choose SEP over emsisoft. A well configured SEP is very powerful and light, hence the reason why every Fortune 500 company uses Symantec. However, if your SEP is an unmanaged version and you did not install all the policies supplied by Symantec to paying customers, then you would be better of with emsisoft. Emsisoft and its behaviour blocker is very good too.
Choosing which AV to install would depend on whether your Symantec Endpoint Protection was well configured. If your symantec endpoint protection is managed by your company, with all the system hardening policies, firewall policies in place, I would choose SEP over emsisoft. A well configured SEP is very powerful and light, hence the reason why every Fortune 500 company uses Symantec. However, if your SEP is an unmanaged version and you did not install all the policies supplied by Symantec to paying customers, then you would be better of with emsisoft. Emsisoft and its behaviour blocker is very good too.