Praise be to Allah.
It is rather unusual [in my opinion] to raise this kind of question. We ought to ask ourselves; is it really beyond our reach to have a large enough place, even if it were to be in a park, a stadium, etc., which would be sufficient to cater for the large number of praying people? How were our Muslim ancestors performing their Salaat-ul ‘Eed? Did not they perform it in an open place nearby their town, even though it might have been on a rainy or chilly day, which was the practice of the Prophet (peace be upon him). However, let us assume that the matter is neither due to laziness nor disorganisation, nor due to the fact that they are accustomed to performing Salaat in enclosed places and are not acclimated to performing it in open places. If all the aforementioned is true and the excuse is a valid one, the solution, as Shaikh Abdul-Azeez Ibn Baaz states, is to have numerous places where the Salaat can be performed, not through holding many congregations [at the same place]. This is because if they were to hold a second [or more] Salaat-ul ‘Eed then it would count as if one is performing a missed Salaat, not as performing a Salaat at its due time, even though the Imaam would be changed and the congregation is a different one. Our Shaikh, may Allah benefit us with his knowledge, also stated that in the absence of large enough mosques, one may even resort to the use of houses in different areas to hold Salaat-ul ‘Eed in congregation, and only Allah, ta‘aala, knows best.