You might be surprised on how that would work out.
Say for example the only asset of the corp was bare land in a prime location, basis of 100,000 and fmv of 200,000, clear title.
So B's stock value of 25% = 50,000.
First option is for A to buy B's stock for 50,000 out right if he has the cash, either before or after 1031 transaction with zero boot received.
If he does not have the cash, the property can be sold through a partial 1031 and 50,000 of cash received, which is used to redeem B's stock.
Then a gain of $50,00 is recognized. A's 75% share of the gain is 37,500. Assume the gain is taxed at 15% federal and 10% state for a total of $9,375.
So now instead of spending 50,000 to become 100% owner of corp worth $200,000, he has paid $9,375 in taxes to to become 100% owner of a corp worth $150,000.
A third option is to complete the 1031 in whole, then borrow 50,000 against the replacement property at the corporate level. The $50,00 is then used to redeem the 25% stock owned by B. In that scenario A has not spent any money personally to become 100% owner in a corp worth $150,000, including a note payable of $50,000. Also, "A" does not incur a tax bill under that option.
Hope I am not overlooking anything here, but if you run the numbers for your client he or she will have some solid footing to make a decision.