Is it possible to switch from VFR to IFR and back?

If I am instrument rated and my aircraft is fully equipped for
instrument flight, and I start out a flight with a VFR flight plan,
and it gets foggy enough that I'm below minimums, is there a way to
switch to IFR in flight, or do I have to have filed IFR from the
beginning? If it's possible in flight, how does it work? Is it
possible to later switch back again?

I ask because it seems like it might be practical to start out as VFR
but still have the option of going IFR if the weather turns
unexpectedly poor (at least in terms of visibility or clouds). At the
same time, filing IFR for the whole flight just because part of it
_might_ be in IMC seems like it could be overkill.

This of course assumes that a pilot and aircraft are ready and able to
handle IMC if they encounter it.

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