The decays of the B+ meson to the final state D*D--(s)+pi(+) are studied in proton-proton collision data collected with the LHCb detector at centre-of-mass energies of 7, 8, and 13 TeV, corresponding to a total integrated luminosity of 9 fb(-1). The ratio of branching fractions of the B+ -> D-Ds+pi(+) and B-0 -> D*D--(s)+ decays is measured to be 0.173 +/- 0.006 +/- 0.010, where the first uncertainty is statistical and the second is systematic. Using partially reconstructed D-s*(+) -> D-s*(+)gamma and D-s(+)pi(0) decays, the ratio of branching fractions between the B+ -> D*D--(s)*(+)pi(+) and B+ -> D*D--(s)+pi(+) decays is determined as 1.31 +/- 0.07 +/- 0.14. An amplitude analysis of the B+ -> D*D--(s)+pi(+) decay is performed for the first time, revealing dominant contributions from known excited charm resonances decaying to the D*(-)pi(+) final state. No significant evidence of exotic contributions in the D-s(+)pi(+) or D*D--(s)+ channels is found. The fit fraction of the scalar state T*(c (s) over bar0) (2900)(++) observed in the B+ -> D-Ds+pi(+) decay is determined to be less than 2.3% at a 90% confidence level.