If the relegation-threatened Baggies do register a quadruple of wins between now and the end of the term, it will double the amount for their entire top-flight campaign to date.
With the club having triumphed only once in their last 18 league fixtures and not at all since Mel, who they have now played under seven times, was appointed as boss in January, it appears an unlikely prospect, but the Spaniard has made it clear he has confidence in his players.
That he has also stressed he is not really looking beyond what he regards as a 'must-win' game on Saturday is perhaps of little surprise, given reports have suggested his job is already under threat.
Mel himself has admitted he does not know what will happen to him if West Brom fail to beat Swansea.
And the 51-year-old said: "It is possible to win four more games - and, indeed, win more than that.
"But we just have to think about the next game and winning that one.
"I'm not thinking about there being 10 games, I'm just thinking about there being one game.
"We must take each game as it comes and always be thinking about the next one."
After Swansea, West Brom face Hull and Norwich away either side of hosting Cardiff.
Their other remaining home fixtures are against Tottenham, West Ham and Stoke, and they will also visit Manchester City, Arsenal and Sunderland.
They are currently 17th in the table, clear of the relegation zone on goal difference alone.
And while they have a game in hand over 18th-placed Cardiff, 19th-ranked Sunderland have 12 more matches to go and are only a point worse off than Albion and the Bluebirds.
Mel has overseen three losses and four draws so far, and when it was suggested that his side were sleepwalking towards relegation, he said: "I think the same might be said of the other teams that are down there, not just West Brom.
"But with 30 points still to play for, I also think it's too soon to be speaking like that."
Then asked if he had been shocked by the difficulty of the situation he had walked into by taking the Albion job, the former Real Betis coach said: "No - I have been in similar situations before in Spain.
"The only way to get out of the situation is by working hard.
"And I want all of the pressure to fall on me, rather than it falling on the players."
West Brom have several players unavailable for Saturday's match due to injuries.
Steven Reid (knee), Claudio Yacob (hamstring) and captain Chris Brunt (knee) will all be absent after coming off in last weekend's 3-0 home defeat to Manchester United, with the latter subsequently being ruled out of action for five to six weeks having sustained medial ligament damage.
Diego Lugano was already sidelined with a similar problem - he faces three to four weeks out - and Billy Jones (hamstring) is not yet ready to return.
Meanwhile, Nicolas Anelka will begin his five-match suspension after both he and the Football Association declined to appeal against the sanction imposed over his 'quenelle' goal celebration.