Deals for Argentine forward Mauro Zarate and Senegal international Cheikhou Kouyate have already been wrapped up, adding a goal-threat to the attacking unit and bite to the midfield.
Allardyce is, however, aware of the need to continue reshaping his ranks in the wake of West Ham's struggles in 2013/14.
He has the full backing of his board to pursue top targets, with investment required if performances and results are to be improved.
A number of bids are currently on the table, with West Ham now waiting on replies.
Allardyce is hoping he will receive positive news on the transfer front in the near future, with additions being sought from back to front.
He told West Ham TV: "We've made many bids and there are many negotiations ongoing.
"We particularly want a left-back, ideally another centre-back, a midfielder and at least two more for the front line."