  We have studied the interactions of the scalar resonances f_0(980) and
a_0(980) with the vector resonance \phi(1020) and with the lightest
pseudoscalars \pi, K, \eta and \eta'. We first obtain the interaction kernels
without including any new free parameter. Afterwards, the interaction kernels
are unitarized and the final S-wave amplitudes result. We find that these
interactions are very rich and generate a large amount of pseudoscalar
resonances including the K(1460), \pi(1300), \pi(1800), \eta(1475) and X(1835)
resonances. The f_0(980)\phi(1020) self-interactions give rise to the
\phi(2170) resonance. For realistic choices of the parameters we also obtain an
isovector companion in the same mass region from the a_0(980) \phi(1020)
interactions.
