I have hi-end mainboard (Z87) with 7 PCI-E slots.
I can't use more than 6 videocards on it.
Theres's a lack of PCI-E lines.
Z87 supports up to 8 PCI-E lanes. Check the spec here
http://ark.intel.com/products/75013.
But in your case, there could have been a limitation in the motherboard itself in how it assigns resources to the various devices on it.
PCI-e Express 1X to 3 Port 1X card? - pointless, same reason.
I've read forum posts where it was possible to use the PCI-e Express 1X to 3 Port 1X card to run 8 GPUs on a 6 PIC-E slot motherboard. Search the Ethereum forum to see for yourself.
More than 6 - only on X79, X99 etc...
Any chipset that supports 8 lanes can theoretically support more than 6 GPUs. MSI Z97 Gaming 5 board can run 7 GPUs using its 7 PCI-E slots (as documented by Cryptomined on his YouTube channel), but people have found that it's generally not worth the effort. It's wise to save time and effort by running 6 cards on motherboards without too many bells and whistles.