The uncertain fate of the troubled John Muir & Co. , came close to resolution today as its management fashioned an acquisition agreement for at least part of the firm with a little-known brokerage house.

Rooney Pace Inc. agreed in principle to acquire Muir's office at 61 Broadway and Muir's New York accounts .Muir, in the joint announcement, said it expected the transaction to be confirmed by the weekend and that by Monday, Rooney Pace should be operating from the Broadway office.

In a separate announcement, Herzfeld & Stern said it would take over the lease on Muir's Sarasota, Fla., office and hire the two Muir employes there. A source at Herzfeld & Stern said that no money was paid to Muir and that both members of the two-person office were hired mainly because they are friends of a Herzfeld & Stern official.

The outlook of the other offices in Muir's national network, including a major one in Washington, remains uncertain. A source in the Washington office said that salesmen there were assuming that the office would be closed.

Late last week, Muir's general partner, Raymond L. Dirks, went to the New York Stock Exchange and said the firm wanted to sell off its retail accounts. In recent months, Muir has been hit by a number of lawsuits by investors in some of the record 45 new issues of common stock Muir has sold to the public in the past 20 months.

Dirks told the exchange that the combination of the lawsuits and bad publicity was causing the firm's top sales personnel to defect. Another problem is that Muir also has been under investigation by the Securities and Exchange Commission.

The exchange called Merrill Lynch & Co. and other major brokerages to seek someone to take over the foundering Muir firm.

Earlier in the week, Thomson McKinnon Securities Inc. was interviewing Muir brokers and reviewing the firm's books. But the bigger firms apparently decided against taking on Muir's 80,000 accounts or its sales staff.

Apparently, the only suitor that could be found so far was the small Rooney Pace firm.