By Francesco Guarascio and Alastair Macdonald

BRUSSELS (Reuters) - Just as it starts to grapple with the profound institutional upheaval that is Brexit, the European Union faces a potential game of musical chairs in top jobs which senior figures are trying to contain.

The end of Martin Schulz's mandate as EU parliamentary speaker in January risks triggering a free-for-all battle among political parties and member states for influence not only in the legislature but other EU institutions in the coming year.

That would add to existing tensions that have left the bloc struggling to agree common responses to problems ranging from debt-strangled growth in the euro zone and a wave of Syrian and other refugees to negotiating the Britain's complex EU exit.

Backroom jockeying for power among politicians unknown to most of the Union's half-billion citizens would also not enhance the reputation of institutions fighting to reverse the anti-EU, nationalist surge seen in Britain's June referendum and set to play a big role in German, French and Dutch elections in 2017.

Two years ago, Schulz's center-left group promised that the German Social Democrat would give way for a conservative successor; but this would now give the right the presidencies of all three major EU bodies, with Luxembourg's Jean-Claude Juncker running the executive European Commission and Donald Tusk of Poland chairing EU summits as president of the European Council.

Tusk's own mandate expires at the end of May but he is expected to want to stay on. This week Juncker, who has three years left, appealed to conservative allies not to oust Schulz, with whom he has forged a left-right "grand coalition" to back legislation.

"If you are crossing difficult times and troubled waters, stability is of the essence," he told France 24 television during a joint interview with Schulz. The trio of himself, Tusk and Schulz was working well, Juncker said, and should carry on.

Schulz, who admirers say has raised the profile of the European Parliament in two terms as president over the past five years, refuses to say if he will step down as agreed though aides say he does not rule it out.

Adding to uncertainty is whether he might find a new role challenging center-right Chancellor Angela Merkel in Germany's parliamentary election a year from now.

"There are a lot of people thinking about my future, amongst them some who say I'm doing a good job. I find this not so bad," Schulz told France 24 when asked whether he would seek a third term. But he declined to say more on whether he would run again.

If Schulz were replaced by a center-right figure, diplomats say, it could trigger a chain reaction, notably against Tusk -- although there is precedent for one party having all three jobs.

Aides to the Pole, who took office in late 2014, say he is not yet thinking about what do when his term expires. It has been widely assumed that he would serve at least five years. A renewal needs only a majority of EU leaders, meaning that his own right-wing successor as Polish premier cannot block him.

Diplomats say there is little appetite for change, either in Parliament or the Council: "This is all we need, this musical chairs at the top of the institutions," one senior EU diplomat said of the bloc's troubles with Brexit and other crises.

Ousting Schulz could upset things and should be avoided, the diplomat added: "Right now we have balance. We should keep it."


Merkel herself has stayed out of the debate on Schulz but her allies in the European Parliament's European People's Party (EPP) have newly agreed to put up a candidate for the speaker's chair, to be voted on by lawmakers in January. The biggest of eight blocs in the chamber with 215, or 29 percent, of the 751 seats, the EPP will choose its candidate in December.

The election for speaker is part of a mid-term reshuffle of parliamentary posts, including committee chairs. An added element of this year's horse-trading will be the fate of the 73 British members, whom some colleagues want to see sidelined and removed from key roles even before Britain leaves the EU.

Center-right officials say Schulz should make way for an EPP president as agreed when the EPP let Schulz win in 2014 as part of deal that saw Parliament back Juncker at the Commission.

Some EU officials have said the center-left S&D, which has 25 percent of seats, could be promised major posts later. Others raise the possibility that other parties, notably the centrist liberals, could bid for the post as a compromise. Schulz has cross-party support in parliament for his efforts to strengthen its legislative role but opponents complain that his double act with Juncker makes the parliament seem soft on the executive.

Another feature of the interplay between competition for EU posts and national elections next year is the fate of another president of a key political institution - the center-left president of the Eurogroup of euro zone finance ministers.

Dutchman Jeroen Dijsselbloem faces an uncertain future after a national election in March. Should he lose his portfolio in a new governing coalition in The Hague, that could cost the S&D another key post if conservatives sought to chair the Eurogroup.

(Editing by Dominic Evans)