Apple may only need to wait until Tuesday to get early clues about its chances of success in the biggest tax case in recent history.

The iPhone maker has been arguing its case at the European Union's General Court to topple a record 13 billion-euro ($14.3 billion) E.U. tax order. This week the same panel of judges will deliver a ruling on two smaller but related challenges by Starbucks and a Fiat Chrysler Automobiles unit.

They are the first in a series of cases to come to a decision as companies rail against E.U. antitrust chief Margrethe Vestager's five-year crackdown on allegedly unfair tax deals.

While the facts of the various appeals differ significantly, Tuesday's decisions "should have a far-reaching effect, both on the other pending cases and going forward," said Howard Liebman, a tax partner at law firm Jones Day in Brussels, Belgium, who isn't involved in the disputes.

The judges' stance will "presumably establish some precedent as to how far the court is willing to allow the commission to extend its approach of judging tax regimes — and individual tax rulings — in the context of a state-aids analysis," he said.

Appeals have been piling up at the E.U. courts since state-aid investigators started work in 2013 to unearth what they deem to be the most problematic examples of otherwise legal individual tax agreements doled out to companies by countries.

The judges' verdicts could empower or halt Vestager's inquiries, which are now centering on fiscal deals by and Alphabet.

Starbucks and Fiat were targeted on the same day in 2015 by a similar E.U. order to pay back about 30 million euros each over their tax arrangements in the Netherlands and Luxembourg respectively.

The commission decisions accused Luxembourg and the Netherlands of granting so-called tax rulings to the companies that backed "artificial and complex methods" to calculate their taxable profits but that didn't reflect "economic reality."

The E.U. said at the time that the companies did this by setting prices for products and services sold between units — called transfer prices — that didn't reflect market conditions.