As they trail by two goals following last week's opener in Rome, La Real have the odds stacked against them when they meet Jose Mourinho's men.
Match preview
An eventful first leg at Stadio Olimpico saw Real Sociedad one goal down as early as the 13th minute, when Stephan El Shaarawy pounced at close range following a rapid Roma counter; Marash Kumbulla's late header from Paulo Dybala's corner then sent the Spanish side home facing a potential Europa League exit.
Take Kubo and Andrea Belotti struck the woodwork for either side between the hosts' two strikes, but having conceded just twice in six group-stage games, La Real had shipped as many again within the space of 90 minutes.
The Basque club have now won just one of their seven matches against Italian clubs in European competition, but will have to defy that record on Thursday, when their dreams of European glory are at stake.
Coach Imanol Alguacil has acknowledged that Roma will surely sit back, soak up pressure and strike on the break - and also from set-pieces. Punishing any lapses at the other end, though, may not be so simple, as his team are suffering a sticky patch which threatens to derail a so-far successful season.
Following Sunday's 1-1 draw with Mallorca, a four-game winless run in La Liga leaves them clinging on to fourth place in the standings, and the San Sebastian side - who have never made it further than the quarter-finals in either the Europa League or its predecessor, the UEFA Cup - have scored only twice in their last five matches.
From Roma's perspective, perhaps the only negative aspect of a job soundly done last week was a head injury suffered by captain Lorenzo Pellegrini, who had to be withdrawn on the hour mark.
Otherwise, the Giallorossi's love affair with continental competition continues under the watch of Jose Mourinho, who is a past master in Europe, and they are now close to following last year's Europa Conference League triumph with a place in the last eight of the Europa League.
History is certainly on their side, as not only have the Eternal City side now scored in 35 of their last 36 European matches but they have also have progressed from all five previous Europa League ties after winning the first leg.
Mourinho's record stacks up quite favourably, too, as he has lost only two of his 16 games in the competition's knockout phase, but the wily tactician will be hoping the effects of recent domestic difficulties do not bleed into Roma's pursuit of more silverware.
Either side of beating Real Sociedad and Serie A rivals Juventus, they have lost to Cremonese - who also knocked them out of the Coppa Italia earlier this year - and, on Sunday, Sassuolo.
The latter defeat came in a madcap encounter, during which Roma trailed 2-1 when Marash Kumbulla was sent off for a senseless swipe at Domenico Berardi, before Paulo Dybala gave the 10-man Giallorossi hope with a second-half howitzer - hope extinguished by conceding a fourth goal in the 75th minute to ultimately lose 4-2.
A rather calmer affair would be Mourinho's preference upon his return to Spain - scene of several successes while managing Real Madrid - and 'parking the bus' is a strong possibility as he stalks the touchline again, following his latest Serie A suspension.
Real Sociedad Europa League form:
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Real Sociedad form (all competitions):
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D
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Roma Europa League form:
D
W
W
L
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Roma form (all competitions):
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L
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L
Team News
Roma's plans to hold their hosts at bay have been boosted by news that Lorenzo Pellegrini should be available after going through concussion protocols, having missed Sunday's game with the head injury he suffered last Thursday.
After being withdrawn at half-time against his former club, ex-Real defender Diego Llorente is set to make a return to San Sebastian, while Andrea Belotti is now back from a hand injury and Roger Ibanez can play following a European suspension.
Belotti is yet to score in Serie A this season, so another off-form striker, Tammy Abraham, should start instead; Marash Kumbulla is facing a domestic ban - ruling him out of Sunday's Derby della Capitale - but could still feature in the visitors' back three.
Real Sociedad, meanwhile, welcomed talisman David Silva back to their starting XI last week after missing six games with a calf problem, and the former Manchester City playmaker is set to play a role in their attempted comeback at Anoeta.
Brais Mendez will expect to start, too, after he was benched at Stadio Olimpico; the Spain international has created 16 chances in the Europa League this season, more than twice as many as any other La Real player.
Aritz Elustondo and ex-Roma striker Umar Sadiq are still out injured, while 13-goal top scorer Alexander Sorloth should return up front after being rested on Sunday.
Real Sociedad possible starting lineup:
Remiro; Gorosabel, Zubeldia, Le Normand, Rico; Zubimendi, Merino; Oyarzabal, Silva, Kubo; Sorloth
Roma possible starting lineup:
Patricio; Mancini, Smalling, Llorente; Karsdorp, Cristante, Matic, Zalewski; Wijnaldum, Dybala; Abraham