It is generally agreed in buddhist tradition that two Buddha can not arise in the same lokadhatu (world system) at the same time.
Lokadhatu has many interpretation, the traditional description equate it with 10^9 sun - moon - earth.
The commentary that I read, but now I forget the name, explain the reason why:
- The world cant support the might of two Buddha
- If two Buddha arise at the same time, people might compare them
- One will trust one Buddha and disrespect the other one.
On the other hand, the criteria of the same world system create an exception: There may be more Buddha outside this world system. This is the argument that create the basis of many other Buddha in later Buddhism.
The treatise Maha Prajna Paramita Sastra commented:
Thus, a sūtra has said that “two Buddhas cannot appear together in the same world”, but by ‘the same world’ the sūtra does not mean to designate all the universes of the ten directions. The sūtra also says that “two cakravartin kings are not found in the world together”; it does not mean to say that two cakravartin kings cannot coexist in the same trisāhasramahāsāhasralokadhātu; it says only that two cakravartin kings cannot coexist in the same cāturdvīpaka (universe of four continents). It is necessary to aquire very pure merit (punyaviśuddhi) in order to reign over the entire world without encountering a rival [as is the case for the cakravartins]. If there were two kings [in the same world]. that would mean that their merit was not pure. Similarly, although the Buddhas have no feeling of jealousy (īrṣyā) one against the other, over lifetimes they have accomplished such pure actions that they cannot both appear in the same world (lokadhātu), namely, in the same trisāhasramahāsāhasralokadhātu consisting of a a million Mount Sumerus, a million suns and moons
In the Tsa a han king (Saṃyuktāgamasūtra),[15] it is said: “When it is pouring rain, the rain drops (bindu) are so close together that they cannot be counted. It is the same for the universes (lokadhātu). In the east (pūrvasyāṃ diś), I see innumerable beings born, subsisting and perishing. Their number is very great, defying calculation. It is the same in the ten directions. In these universes of the ten directions, innumerable beings undergo the threefold physical suffering (kāyaduḥkha), old age (jarā), sickness (vyādhi) and death (maraṇa); the threefold mental suffering, desire (rāga), hatred (dveṣa) and ignorance (moha); and the threefold suffering of rebirth (punarbhavaduḥkha), rebirth among the damned (naraka), the pretas and animals (tiryagyoni). All of these universes have three types of men, inferior (avara), middling (madhya) or [126a] superior (agra). Inferior men are attached (sakta) to present happiness, middling men to future happiness, superior men seek the Path; they are filled with loving-kindness (maitrī) and compassion (karuṇā) and have pity for beings.” When the causes and conditions [necessary for the coming of a Buddha] are present, why would the effect, [namely, the coming of a Buddha] not be produced? The Buddha has said: “If there were no sickness, old age and death, Buddhas would not appear.”[16] That is because when one sees people tormented by old age, sickness and death, one makes the resolution (praṇidhāna) to become Buddha in order to save all beings, cure their mental illnesses and take them out of the pain of rebirths. Now, precisely these universes of the ten directions show all the causes and conditions required for the coming of a Buddha (buddhaprādurbhāva). How can you say that our universe is the only one to have a Buddha and the others do not? You merit as little credence as the person who says: “Here there is wood, but there is no fire; the ground is wet, but there is no water.” It is the same for the Buddha. These beings suffer the pains of old age, sickness and death in their bodies; their minds are subject to the sicknesses of desire (rāga), hatred (dveṣa) and ignorance (moha); the Buddha appears in the world to destroy this threefold suffering and introduce beings into the triple vehicle (yānaytraya). How could the Buddha not appear in all the universes where this suffering exists? It would be wrong to say that s single remedy (agada) is enough to cure numberless blind people (andhapuruṣa) [and consequently, a single Buddha to cure numberless beings]. Therefore the Buddhas of the ten directions must necessarily exist.
their arguments can be read fully in Act 9.2: Examination of the plurality of Buddha