Years ago (too many to mention numbers), I helped write a campaign that included many half races.
In addition to the normal half-breeds (1/2 elf and 1/2 orc), we had:
Dwonome (1/2 dwarf, 1/2 gnome)
Gnomling (1/2 gnome, 1/2 halfling)
Half-Dwarf (1/2 dwarf, 1/2 human)
Tarnat (1/2 dwarf, 1/2 orc)
Ulf (1/2 elf, 1/2 dwarf)
Gnoblin (1/2 deep gnome, 1/2 [psionic] blue goblin)
Half-Dragon (1/2 dragon, 1/2 human or demihuman (including half breeds but no goblinoids or orcs) [These were our only possible 1/4 breeds]
But orc/elf combo, never considered it.
We had a half-breed template that took care of other races we hadn't considered.
We also house-ruled that most (95%) half-breeds are sterile. If someone wants to play a 1/4 breed for 1/2 dragon, they can; but there are no other 1/4 breed racial combinations.
I do have rules for all these half-breed races if anyone is interested.