Upgrading a Celeron 420 processor to a Celeron 440 may be possible by simply replacing the CPU, but compatibility depends on the motherboard. It's essential to check the motherboard manufacturer's website to confirm if it supports the faster processor and whether a BIOS upgrade is necessary. Generally, CPUs do not require drivers, and the performance boost from this upgrade would be minimal, as both processors share similar specifications aside from the bus multiplier. A more significant performance increase could be achieved by upgrading to a higher architecture, such as a Pentium D805 or D915, which would provide a greater frequency increase and larger L2 cache. However, this would also result in increased heat dissipation and power consumption, potentially up to three times more than the current setup.