Partnership agreement. For the purposes of subchapter K, a partnership agreement includes the original agreement and any modifications thereof agreed to by all the partners or adopted in any other manner provided by the partnership agreement. Such agreement or modifications can be oral or written. A partnership agreement may be modified with respect to a particular taxable year subsequent to the close of such taxable year, but not later than the date (not including any extension of time) prescribed by law for the filing of the partnership return. As to any matter on which the partnership agreement, or any modification thereof, is silent, the provisions of local law shall be considered to constitute a part of the agreement.