(Reuters) - Less than a month after he appointed a client of Levi & Korsinsky's to lead a securities class action against Tesla and CEO Elon Musk, U.S. District Judge Edward Chen signaled he’s having second thoughts about his decision.

Levi & Korsinsky was facing a January deadline to file an amended complaint on behalf of Tesla investors who allege they were defrauded by Musk’s infamous Twitter claim to have secured financing to take his company private at $420 per share. But in a docket entry last Thursday, Judge Chen stayed the deadline for the amended complaint and told Levi & Korsinsky to wait until he has had a chance to decide the merits of two motions asking him to reconsider the appointment of the firm’s client as lead plaintiff.

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Levi & Korsinsky represents an individual Tesla investor, Glen Littleton, who claims to have lost $3.5 million in Tesla investments as a result of Musk’s tweet and subsequent statements. Judge Chen selected Littleton and his lawyers after a hearing last month in which several candidates to lead the case emphasized the potential conflicts for traditional long investors and Tesla short sellers. In his order appointing Littleton, the judge said the Levi & Korsinsky lawyer was well suited to represent all kinds of Tesla investors – longs, shorts and options traders – because he held a variety of Tesla positions.

Within days of Littleton’s appointment, Robbins Geller Rudman & Dowd and Lieff Cabraser Heimann & Bernstein moved for reconsideration. On behalf of their client, an individual investor named Dany David, the firms argued that Littleton actually made money on Tesla trades in the timeframe allegedly tainted by Musk’s tweet. Littleton’s lawyers could only claim a loss on their client’s investment, according to the Robbins Geller and Lieff Cabraser motion, by counting losses on securities he bought before the notorious tweet and sold during the class period.

According to the reconsideration motion, Judge Chen’s order appointing Littleton to serve as lead plaintiff “erroneously determined that Mr. Littleton was not a net seller/net gainer based on his options and short positions. In fact, Mr. Littleton is a net seller/net gainer precisely because of those positions, and should not have been appointed lead plaintiff.”

The David reconsideration motion was quickly followed by a second motion asking Judge Chen to rethink the appointment. The second motion, filed by Kahn Swick & Foti for a fund called Bridgestone Investment, argued that Judge Chen should not have considered Littleton’s argument that the fund’s purchase of call options projecting a $450-per-share price for Tesla stock could not have been motivated by Musk’s tweet about a $420-per-share deal. Littleton, according to the Bridgestone filing, claimed losses on precisely the same sort of investment. So, according to Bridgestone, since its alleged total losses exceeded Littleton’s total losses, and both claimed losses based on call options purchased before Musk’s tweet, Judge Chen should have selected Bridgestone.

It’s quite rare for shareholders’ firms immediately to ask judges to reconsider their lead plaintiff and lead counsel selections. But Judge Chen didn’t dismiss the arguments out of hand. Instead, he instructed Levi & Korsinsky to respond to the motions – and then put off the deadline for filing an amended complaint.

In its response to the motion by Robbins Geller and Lieff Cabraser, Levi & Korsinsky said sellers like Littleton are part of the class. “Both purchasers and sellers of options may have suffered losses as a result of defendants’ fraud and should be represented by the lead plaintiff,” the brief said. “As Littleton suffered losses both purchasing and selling options, as well as buying stock, and from both long and short positions, he provides this representation.” The brief also said Robbins Geller and Lieff Cabraser were reviving arguments they’d already made before Judge Chen picked Littleton as lead plaintiff. Those arguments “therefore should be easily denied by the court, which has already considered and correctly rejected” them.

Nor did Bridgestone raise any new arguments in its motion for reconsideration, according to Levi & Korsinsky’s separate response to the motion by Bridgestone’s lawyers at Kahn Swick. Judge Chen picked Littleton, the filing said, because he held different sorts of positions in Tesla and could represent the interests of long, short and options investors. Bridgestone only held a short position, the response said, so it “is neither adequate nor typical of a class consisting in substantial part of investors who lost money from short positions.”

Judge Chen said he would decide whether to hold a hearing on the reconsideration motions after he’s had a chance to read the briefs. Investors said at the lead plaintiff hearing last month that Tesla’s exposure could top $1 billion in the class action, though Tesla’s lawyers at Fenwick & West said they plan to move to dismiss the allegations.

I emailed Nicholas Porritt and Adam Apton of Levi & Korsinsky for comment on the reconsideration motions but didn’t hear back.