There is little left that Carillion can do ahead of the 'put up or shut up' deadline in its pursuit of infrastructure specialist Balfour Beatty, according to analysts at Liberum Capital, after the latter rejected a sweetened proposal from the construction group on Wednesday.Balfour said that Carillion's latest approach was not in its shareholders' best interests, noting that the third offer was only a "small value change" from the preceding bid.The Balfour board again questioned the "considerable risks" around plans to significantly reduce the scale of the UK construction business "when it is poised to benefit from a recovery in the market", and again dug in its heels about its intention to sell its US-based Parsons Brinckerhoff (BP) subsidiary."Carillion has indicated it will not go hostile. There is little (if anything) Carillion can do ahead of tomorrow's deadline," Liberum wrote."Carillion's final throw of the dice is to try to persuade 50% of the Balfour Beatty shareholder list to vote down the PB sale at EGM - a very risky strategy for Balfour shareholders," the broker said.Under UK takeover rules, as long as there isn't another bid from a third party, Carillion will not be allowed to make another approach until February 2015.As for Balfour, Liberum rates the stock as a 'buy' and said that Carillion's approach will have reminded the market of the long-term value at the group."Meanwhile the PB disposal is progressing well (press reports a valuation of above £700m), a new CEO is (said to be) close to being appointed, the investment portfolio is expected to be valued at in excess of £1bn and a strategy to return margins towards 2% is emerging."It also said Carillion shares were a 'buy', saying that the company has excellent order book momentum, shrinking leverage and an undemanding valuation. "Carillion may have been weakened by showing its desire to do a deal so publicly but the stand-alone story remains attractive."Balfour's shares were down 6.4% at 239.6p by 09:24, while Carillion was 2.5% lower at 328.2p.BC