What is Dish Network’s chairman, Charles W. Ergen, up to?

That question took on new significance on Wednesday evening, as Dish announced a plan to raise its tender offer for shares in Clearwire to $4.40 a share in cash. The bid trumps the most recent takeover offer by the company’s majority owner, Sprint Nextel, of $3.40 a share, less than two days before shareholders are set to vote on the latter offer.

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In a letter to Clearwire’s board, Dish reiterated the superiority of its offer for the company and stressed its desire to harness the wireless network operator’s spectrum to its own holdings.

Dish is seizing upon continued investor dissatisfaction with Sprint’s revised bid, which came after shareholders roundly criticized previous proposals as insufficient. Sprint — with the backing of its Japanese suitor, SoftBank — sweetened its offer to head off defeat.

(That said, Sprint has struck agreements with several big shareholders that will give it a 65 percent stake in Clearwire even if its offer is rejected.)

In a statement on Wednesday, Clearwire said: “The special committee of Clearwire’s board of directors has received Dish Network’s offer and will review it to determine the best course of action for the company and its stockholders. The special committee has not made any determination to change its recommendation of the current Sprint transaction.”

It isn’t clear what Mr. Ergen is trying to accomplish. Clearwire disclosed in a regulatory filing last week that it had not held substantive conversations with Dish in a month. Furthermore, Sprint owns more than 50 percent of the smaller wireless company and is unlikely to sell out its holdings, since it considers Clearwire an important part of its own turnaround efforts.

Indeed, much of Dish’s attention in recent weeks appeared focused on its $25.5 billion bid for Sprint itself, hoping to wrest the bigger network company away from SoftBank. Dish has provisionally lined up about $9 billion in bank loans to support that offer and is conducting due diligence.

But some people involved in the process have questioned whether Mr. Ergen has again switched his main efforts back to amassing a significant minority position in Clearwire, forcing Sprint to cut a deal to gain control of the company.

Shareholders of Sprint are scheduled to vote on the SoftBank bid for the company on June 12.