Termite damage

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Hi All, first time posting to the forum and would love to get some termite advice from those who’ve had experience. We’re about to go into contract on a 25′ wide attached 2 story townhouse in Forest Hills, and while we know the house needs extensive renovation, we discovered that there’s heavy termite damage. It appears to be mostly in one room on the street side of the house along the party wall. A few joists are pretty well eaten through, but it seems that the damage skips around–other neighboring joists appear to be sound.  Some of this is visible from the first floor, but since the basement ceiling is sheetrocked (apart from some places where holes have made for spot treatment), it’s hard to get a full view of all the joists in question.  The center beam is a steel I-beam, so no issues there.  Overall the house looks pretty pretty rough, but the floors and walls throughout are level and plumb and feel very solid.  There might be the slightest give in the floor where the damage is centered.  The house has been vacant for the last six years, and according to the listing agent, the termites were treated then.  The house also has lots of old water damage, but it got a new roof about six years ago and seems dry.  The damaged sections seem papery and very dry, but I have no way of telling whether this is old damage or whether the termites are still active. We have an engineer’s inspection (Heimer) on Wednesday.  Per their website, all inspectors are qualified to assess for termites, but is it worth calling in a specialist? Has anyone faced a similar situation?  How was it repaired, and can you give a general sense of cost? Thanks all, and I’ve attached a picture of one of the joists in question.