I think the primary constraint is having a place to keep them. I've owned over 20 bikes and the largest the on-hand fleet ever grew to was 14 riders not including frames hanging on walls that will never be ridden. I've finally let 7 of the riders go on to new homes over the past few years... sniff, sniff.

Recently departed include:

'97 ProFlex 857 (Actually, this one is still hanging in the garage but was given to our son)
'92 Diamondback
'87 Kuwahara Cougar
'84 Raleigh Prestige
'84 Raleigh Gran Prix
'85 Raleigh Custom
'00 Ventana El Conquistador

The 7 rideable keepers include 2 road tandems, 3 road bikes (one is my wife's), an off-road tandem, and my off-road 1/2 bike.