What options can I specify for Java on z/OS?

You can use the following command to list them all.

java -X -help 

On Java 8 SR 8 this gave me

The following options are non-standard and subject to change without notice. 
                                                                                                       
  -Xbootclasspath:<path>    set bootstrap classpath to <path> 
  -Xbootclasspath/p:<path>  prepend <path> to bootstrap classpath 
  -Xbootclasspath/a:<path>  append <path> to bootstrap classpath 
                                                                                                       
  -Xrun<library>[:options]  load native agent library 
                            (deprecated in favor of -agentlib) 
                                                                                                       
  -Xshareclasses[:options]  Enable class data sharing (use help for details) 
                                                                                                       
  -Xint           run interpreted only (equivalent to -Xnojit -Xnoaot) 
  -Xnojit         disable the JIT 
  -Xnoaot         do not run precompiled code 
  -Xquickstart    improve startup time by delaying optimizations 
  -Xfuture        enable strictest checks, anticipating future default
  -verbose[:(class|gcterse|gc|dynload|sizes|stack|debug)] 
                                                                                                       
  -Xtrace[:option,...]  control tracing use -Xtrace:help for more details 
                                                                                                       
  -Xcheck[:option[:...]]  control checking use -Xcheck:help for more details 
                                                                                                       
  -Xhealthcenter  enable the Health Center agent 
                                                                                                       
  -Xdiagnosticscollector enable the Diagnotics Collector 
                                                                                                       
  -XshowSettings                show all settings and continue 
  -XshowSettings:system 
                      (Linux Only) show host system or container 
                      configuration and continue 
  -XshowSettings:all            show all settings and continue 
  -XshowSettings:vm             show all vm related settings and continue 
  -XshowSettings:properties     show all property settings and continue 
  -XshowSettings:locale         show all locale related settings and continue 
                                                                                                         
Arguments to the following options are expressed in bytes. 
Values suffixed with "k" (kilo) or "m" (mega) will be factored accordingly. 
                                                                                                         
  -Xmca<x>        set RAM class segment increment to <x> 
  -Xmco<x>        set ROM class segment increment to <x> 
  -Xmn<x>         set initial/maximum new space size to <x> 
  -Xmns<x>        set initial new space size to <x> 
  -Xmnx<x>        set maximum new space size to <x> 
  -Xmo<x>         set initial/maximum old space size to <x> 
  -Xmos<x>        set initial old space size to <x> 
  -Xmox<x>        set maximum old space size to <x> 
  -Xmoi<x>        set old space increment to <x> 
  -Xms<x>         set initial memory size to <x> 
  -Xmx<x>         set memory maximum to <x> 
  -Xmr<x>         set remembered set size to <x> 
  -Xmrx<x>        set maximum size of remembered set to <x> 
  -Xmso<x>        set OS thread stack size to <x> 
  -Xiss<x>        set initial java thread stack size to <x> 
  -Xssi<x>        set java thread stack increment to <x> 
  -Xss<x>         set maximum java thread stack size to <x> 
  -Xscmx<x>       set size (or soft max size if option -XX:SharedCacheHardLimit= is 
                  present) of new shared class cache to <x> 
                                                                                                        
   -Xscminaot<x>   set minimum shared classes cache space reserved for AOT data to <x> 
   -Xscmaxaot<x>   set maximum shared classes cache space allowed for AOT data to <x> 
   -Xmine<x>       set minimum size for heap expansion to <x> 
   -Xmaxe<x>       set maximum size for heap expansion to <x> 
                                                                                                        
 Arguments to the following options are expressed as a decimal from 0 to 1. 
 A value of 0.3 represents a request of 30% 
                                                                                                        
   -Xminf<x>       minimum percentage of heap free after GC 
   -Xmaxf<x>       maximum percentage of heap free after GC

 Arguments to the following options are expressed a decimal numbers. 
                                                                                                                
   -Xgcthreads<x>                set number of GC threads 
   -Xnoclassgc                   disable dynamic class unloading 
   -Xclassgc                     enable dynamic class unloading 
   -Xalwaysclassgc               enable dynamic class unloading on every GC 
   -Xnocompactexplicitgc         disable compaction on a system GC 
   -Xcompactexplicitgc           enable compaction on every system GC 
   -Xcompactgc                   enable compaction 
   -Xnocompactgc                 disable compaction 
   -Xlp                          enable large page support 
   -Xrunjdwp:<options>           enable debug, JDWP standard options 
   -Xjni:<options>               set JNI options 
                                                                                                                  

I noticed that some products using Java have the nice option

-Xoptionsfile=/var/xxxf/configuration/colin_override.cfg

Where the file has a list of JVM options one on each line.

This option is not generally available.