Within model-data comparison under a data assimilation (DA) perspective in paleoclimate we may have two main objectives: a) to conduct climate field reconstructions (CFR), and b) to constrain (or calibrate) the model parameters with the alternative/additional goal of improving model projections of future climates. One can well approach the problem of CFR for past climates without explicitly accounting for parameter estimation, and in fact this has allowed the use of the so-called offline (possibly multi-model) DA approaches for CFR in recent studies. However, in general, for long-term past climate reanalyses, inaccurate parameters in the climate model have a predominant role in the growth of prediction errors. Although DA is most often used for state estimation, combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed, it is also possible to use DA techniques for the joint state-parameter estimation problem. Unfortunately, it is not possible, in general, to use offline approaches for this, as the background ensemble has not been explicitly designed with the joint estimation problem in mind. This leads to the problem that one needs to resort to new paleo-simulations if we want to attempt both (a,b) goals, with the attached computing cost. Here we explore some ensemble strategies for the joint state-parameter estimation problem with a synthetic study using the global Community Earth System Model (CESM v2.1) and MARGO-like sparse pseudo-proxy SST observations.