  In this work we deal with thick brane solutions in the warped
five-dimensional braneworld scenario with a single extra spatial dimension of
infinite extent, for a class of modified theories of gravity with a Lagrange
multiplier. We first present the action, describe the gravity and field
equations, outline a strategy to find explicit solutions and explore the
stability of the gravitational sector. The investigation deals mainly with the
construction of a first order framework capable of using a single scalar field
to simulate warp functions that appear in two-field models. In particular, we
find specific symmetric and asymmetric brane configurations that engender
asymptotic profiles with symmetric and asymmetric five-dimensional anti-de
Sitter geometries. Thus, including a Lagrange multiplier unveils an alternative
approach to induce brane structure using a single scalar field, tracing out new
avenues of research in braneworld scenarios, naturally leading to interesting
results for the localization of matter fields in the brane.
