Can international consortiums without headquarters in Spain occur?
Of course, international consortiums without headquarters in Spain can be launched to the adventure of presenting public tenders here. It is not necessary to have the offices in Gran Vía or anything like that, but eye, you have to be clear about how the game is going and not skip the rules.
The Spanish law, in an open plan, says that foreign companies can get into these processes. The famous public sector contract law (the LCSP, for friends), in its article 56, leaves it very clear: if a company can operate according to the rules of its country and the European Union, ahead with the tender. In summary, if from your country you can sign contracts of that type, in Spain you can also try.
Now, speaking of international consortiums, it is super common for several companies to meet in the Avengers team to go for large contracts abroad. Although they do not have a mailty in Madrid, while meeting the basic requirements, they can participate without problem.
Of course, it is not to arrive and kiss the saint. You have to fulfill things like demonstrating that you can legally hire, that you are not vetoed by the administration and that you have the necessary solvency (come on, that you are not a salehumo). All of that is usually detailed in the specifications of each tender. And you have to read them well, which are not precisely light literature.
A very useful advice (rather almost essential to avoid headaches): have a legal representative in Spain. It is not mandatory, but it helps very much. This crack can deal with paperwork, talk to the administration, resolve fiscal movements and even represent if it is time to fight in court. Basically, the compi that we would all want to have in these situations.
Of course, don't make illusions that it will be easy. There are a lot of competition and companies that know them all. So you have to be well prepared and not leave any loose ends.
So, summarizing the beast: yes, international consortiums without headquarters in Spain can enter the ring of public tenders here, as long as they meet the law and all the requirements. And if you also have someone of trusted carrying your affairs in Spain, everything will be much more shot.