  In this note we define anticyclotomic p-adic measures attached to a finite
set of places S above p, a modular elliptic curve E over a general number field
F and a quadratic extension K/F. We study the exceptional zero phenomenon that
arises when E has multiplicative reduction at some place in S. In this
direction, we obtain p-adic Gross-Zagier formulas relating derivatives of the
corresponding p-adic L-functions to the extended Mordell-Weil group of E. Our
main result uses the recent construction of plectic points on elliptic curves
due to Fornea and Gehrmann and generalizes their main result. We obtain a
formula that computes the r-th derivative of the p-adic L-function, where r is
the number of places in S where E has multiplicative reduction, in terms of
plectic points and Tate periods of E.
