Romania attacks Bulgaria in 1916

  Quite possibly, presuming that the Romanians time it right so they don't simply get stomped by Germany as OTL.  Which further complicated matters for Russia as it increased the length of the east front by about a third. 

  Bulgaria isn't in itself important enough to make much difference.  However if it lead to an attack on E Thrace and the clearing of the straits it might be very important.  [Albeit initially more for the moral boost and possibly avoiding a ruinous attack on the eastern front by Russia keeping the latter on an even keel until the war is pretty much won.

  The other possibly factor with a successful overrunning of Bulgaria is that the western powers have their forces in the Salonika enclave which might come into play here and also if it triggered full Greek intervention, which would add additional forces to the allies in the region. 

  At best if knocking out Bulgaria then puts Turkey into such difficulties they have to come to terms it might start a cascade.  Karl had taken over Austria by about this time and was looking for a way out of the war before the empire collapsed.  He's even more likely to jump at this in such a situation, with the threat of a new Serbian front as well as in Transylvania and possibly either Berlin agrees to a negotiated peace, which would mean some concessions on their part, or if they decide to fight on Vienna makes a separate peace.

  However this assumes that a lot of things go right for the allies.  Not just timing the attack south for when its too late for the Germans to strike through the Carpathians but simply Romania taking out Bulgaria on its own pretty much.  That could be a fairly tough ask to do quickly. 

  It could however go pear shaped as well.  If Romania pulls off a successful attack on Bulgaria and Germany has to plan to attack Romania in the following spring it could force them more onto the defensive elsewhere and as the disastrous Nivelle offensive and its parallel Russian counter-attack showed the allies still had serious problems attacking prepared defenses.  To be fair to the French they had shown better tactics towards the tail end of Verdun and quickly adjusted to a more measured doctrine again but the Nivelle attack nearly broke the French army.  Similarly while better tactics were available what Haig did during the Passchendale offensive markedly increased British losses.  Get the allies too over-confident in early 1917 and things could go even worse.  Then coupled with the rapid overrunning of Romania and collapse of the monarchy in Russia and possibly worse losses in the west things might come apart.