How many lasting outside influences can you get in Iberia? They must be adopted as part of the Iberian identity--using French as a diplomatic language for example does not count.
In OTL, I'd say there were the following:
- Ancient Basque (obvious)
- Ancient Iberian (obvious)
- Celtic/Celtiberian (obvious)
- Punic (mostly just city names, but still an influence)
- Greek and early Roman influences (pre-Christian Romans essentially superseded all the Greek influence, so it's just one)
- Roman Catholic influences (Huge influences from Christianity, but it was a Romanized form rather than straight from Nazareth)
- Visigothic (other tribes left little influence)
- Moorish (Arabic and Berber influence was merged into one over time)
- Medieval Basque (gigantic influence on Castilla, castellano, and the house of Jiménez)
- Renaissance/North Italian (Influences from the Renaissance)
- Habsburg (little effects on the people, but large effects on political organization, the royal family, and Spanish identity)
Possibilities IMO for alternate influences:
- Germanic (Migration tribe influence could have stuck)
- Berber (as separate from Arabic influence)
- Brythonic (the Brythons may have settled Gallaecia, but this meant almost nothing in the long term)
- Byzantine (Byzantine influence could have stuck)
- Persian (Arabs could have adopted more from the Persians, or a dynasty conquering Spain could be Persianized)
- Viking (they could have settled down and formed a "Normandy" or something, they did after all raid various rivers in Iberia)
- Varangian or other mercenary (Mercenaries from the north could settle down somewhere)
- Latin American (Move the capital to Mexico during a foreign occupation; from then on, Spain will be influenced by its former colonies)