If the bitcoin is locked with three private keys using a simple script that involves signing by all three private keys (3 of 3), then there is no way to spend it without providing all three private keys for the signature.
However, bitcoin being a programmable money, it allows you to create a locking script that is decided by time. By that I mean, you can include conditions within your script such that, after x amount of days, you need only 2 keys and after y amount of days you need just one key to spend the bitcoin. Thus, within the broad spectrum of your question, yes the bitcoin can be spent by only one private key that generally requires three private keys, only if the necessary condition is justified in the locking script. Below is the locking script that you will follow to meet the above condition.
<x days> CHECKSEQUENCEVERIFY DROP
<Pub key 1><Pub Key 2><Pub Key 3> 3 CHECKMULTISIG
<y days> CHECKSEQUENCEVERIFY DROP
1 <Pub key 1><Pub Key 2><Pub Key 3> 3 CHECKMULTISIG
The unlocking script for evaluation of
- 3 of 3 will be < Sig 1>< Sig 2>< Sig 3> 1 1. The 1 and 1 at the end indicates evaluating both the first and second IF
- 2 of 3 will be < Sig 1>< Sig 2> 1 0. 1 will trigger the first IF and then the ELSE in the second loop
- 1 of 3 will be < Sig 1> 0 0. It will trigger the first loop ELSE