Some growers may not agree but I always feel that the plant won't do anything that it's not capable of doing. I think your orchid will be fine. You may find that the spikes will have fewer flowers or smaller flowers since the plants energy is being shared by three spikes. On the other hand it may be one of those special crosses that can produce lots of spikes and flowers naturally. I would just give it good care and enjoy the show.
I agree i have 2 Phals that are carrying 3 spikes and yes the blooms are fewer and they spend energy on flowers instead of leaves and roots i will cut all spikes off after the last bloom falls and allow the Phal to rebuild its energy for next season
My question would be whether the new spike appeared before or after you cut the old spike?
Cutting a spike leaving nodes will force the nodes to produce side spikes in some phals. While not all phals respond, those that do can be forced to produce these side spikes even if not strong enough.
However if your new spike appeared after you had done that, then to me it's a clear indicator the plant is strong enough to produce both those forced side spikes AND the new spike. I don't think it would have chosen to start a new one if it wasn't.
I agree with Tucker that generally the plant won't do something it's not strong enough for. However they can also produce spikes/blooms as a 'last ditch' attempt to reproduce when they think they are dying. If the plant looks healthy though I would guess this is not the case. When I've had ones do that, you can really tell the plant is struggling.