i have a theory, but is based on a more strategic Ferdinand I( one of most loved Bulgarian king but a bit noob on diplomacy):
WI begin after the end of the first Balkan war(BW):
-Serbia wants more territories since AH denied Albania
-Bulgaria want Salonika which is occupied from Greece
-OE is a dog liking it's wound waiting to strike back
-Romania want the silistra fortress
Ferdinand I offers Serbia to acknowledge them the occupied territories in Macedonia in exchange of help/support against Greece for Salonika meanwhile, to avoid a second front from a back stab/ revenge from Romania and OE offers to the first the control of silistra for help in case of Ottoman attack. Also Ferdinand send a diplomat to the Russian czar saying he officially renounces to his dreams of a Bulgarian Constantinople, small improvement of the Bulgarian/Russian relations ripped after the first BW.
Both Serbia and Romania accept and basically the second Balkan league is formed while the first one is still composed from Greece and Montenegro( Greece fearing a betray manages to only keep Montenegro in the alliance while Albania doesn't care, the have an AH guarantee).
29 June 1913: Bulgaria Demand the city of Salonika from Greece since Bulgaria did more in the previous war with the Serbians supporting the request, Greece obviously refuses and has already placed his army (150k )on the border with almost a third near the city.
30 June: half of the Serbian army(110k) is placed on the Montenegrin border without attacking, the army doesn't want to lose precious troops fighting partisan an the enemy army (12k) on hostile territory made majorly of mountain paths. The other half of the army is sent with half of the Bulgarian army ( 250k) while the other half is split in 2 groups: 1 of 200k on the chatalja line and the other 50 guarding the Aegean coast from Greece naval invasion.
2 July : the war begin, the Greek army is greatly outnumbered 150k troops against the Bulgar-Serb forces(360k) which are more than twice the size.
5 July : the Greek army resisting but the difference in numbers is to high while the Montenegro army can't attack o help, blocked in their main land.
6 July : the OE tries to get revenge by declaring war and hoping for the Romanian army to back stab Bulgaria for Dobruja
7 July : the Romanians honoring the secret treaty made half a month ago declares his aid for the Bulgarians with Carl I declaring to the press : " our fellow Bulgarian Friends are once again attacked from the oppressing Turks, we won't sit and look but help them against this menace", follows a formal declaration of war against the ottomans but not on the Greeks.
13 July: seeing no other option after losing almost 50k troops Greece surrenders followed from Montenegro
13 July: after some attempts to breach the line ottomans can't try anymore since the Romanian army has joined the Bulgaria army making a total of 600k troops against the 300k Turks
14 July: the Bulgarians with the aid of the Romanian ally starts the catalja offensive
15 July: ottomans are defeated and lost 40k troops, they retreat toward Constantinople, the Balkan forces stay on the line and don't chase them, knowing that an attack toward the city worlds desire would anger the great powers
16 July : Salonika treaty, Greece will recognize the Bulgarian control over the city, also the border with the Bulgarian will be from alexandreia( 50km east Salonika) to ohrid all territories with a good presence of Bulgarians, and Greece renounce to their claims over the region, meanwhile Serbia officially seizes control over north/west halt of Macedonia, and Ohrid due to it's historical importance will become a free city under both Serbian/Bulgarian control
17 July: treaty of Constantinople, ottomans will pay war reparation to Bulgaria and renounce to any claim over Adrianople( odrin in Bulgarian) while Romania takes the silistra fortress as promised, since there weren't any attempts to take the ottoman capital the great powers can't interfere anymore since Russia is already making pressure to leave the Balkans on their own( relation with Serbia are great as in OTL and not bad with Bulgaria).
-----------------------------------------------------------------------------------------------------------------------------------------
with this ATL Balkan war we can see good relation between Bulgarian and Serbians while Greeks and ottomans will grow in revanchism, changing a bit the ww1 Balkan:
same start of the great war but Bulgaria and Romania would likely aid Serbia as member of the Balkan league while Montenegro and Greece would join CP with greeks trying to recover Solnik( Bulgarian name of Salonika) and the OE going for more European holdings( and the other African territories)
stating this a s possible alternative outcome i still don't know id Italy will join the CP or the entente+Balkan league 2.0
any correction will be appreciate, i used the military number list on Wikipedia about OTL second BW
https://en.wikipedia.org/wiki/Second_Balkan_War