Yes, but the new policy and its certificate have to be in force before the old one ends. Any gap between them is reported as a lapse, so the two changes have to overlap rather than meet.
More detail
Switching is often the right move, particularly at the first renewal after a violation, when surcharges have started to decay and the carrier that accepted the record at its worst may no longer be the best price. The mechanics require care. Bind the new policy with an effective date at or before the cancellation date of the old one, confirm the new carrier has transmitted the certificate, and only then cancel. Do not cancel first to avoid double premium for a day; a one-day gap is still a gap. It is also worth confirming that the new carrier actually files, because a cheaper quote from a company that does not handle certificates is not a usable option regardless of price.