The coach industry often will run a duplicate service a few minutes behind if the original serivce got sold out, a long time ago trains did an alike thing too.
Do airlines ever do this? If the 1750 LGW to Berlin flight is full would you ever find an 1800 suddenly appear?
Generally no.
Most importantly, if I sell 220 tickets, am I really going to fly two 189 seat planes to the destination? It doesn't make sense.
There are many more reasons why it doesn't happen.
Many airports are slot limited. You can't just run extra flights to, say, Heathrow unless you have a slot available for it to land and take-off.
Most airlines are also incredibly tight on crew nowadays. Crew planning is a massive operation and it isn't always easy to muster up additional crew to fly at short notice.
Aircraft availability is also very important. There generally aren't many planes sat around - especially in the summer season.
Though most airlines can charter aircraft at pretty short notice. Even Ryanair does private charter work.
For most airlines, upguageing is much more likely. A321 instead of A319 for BA or 737-8Max for Ryanair instead of the class 800.
That's not to say it isn't scheduled to happen sometimes too.
Qatar Airways ran for many years to flights leaving Doha in the early hours and arriving in Heathrow around 6am. An A380 and 77W. For a couple of years both flights left Doha at exactly the same time. The 77W arrived in Heathrow 10/15 minutes earlier as it has a slightly faster cruise, but I would always personally choose the A380 as it is much more comfortable in the economy cabin.
The BA Shuttle has also been mentioned.
You also often see airlines offer additional flights during sporting events/ major events.