  We present a systematic study of the magnetization in YbRh$_{2}$Si$_{2}$
under slightly negative (6?% Ir substitution) and positive (7% Co substitution)
chemical pressure. We show how the critical field $H_{0}$, associated with the
high-field Lifshitz transitions, is shifted to lower (higher) values with Co
(Ir) substitution. The critical field $H_{\mathrm{N}}$, which identifies the
boundary line of the antiferromagnetic (AFM) phase $T_{\mathrm{N}}(H)$
increases with positive pressure and it approaches zero with 6% Ir
substitution. On the other side, the crossover field $H^{*}$, associated with
the energy scale $T^{*}(H)$ where a reconstruction of the Fermi surface has
been observed, is not much influenced by the chemical substitution.}{Following
the analysis proposed in
Refs.\,\cite{Paschen2004,Gegenwart2007,Friedemann2009,Tokiwa2009a} we have
fitted the quantity $\tilde{M}(H)=M+(dM/dH)H$ with a crossover function to
indentify $H^{*}$. The $T^{*}(H)$ line follows an almost linear $H$-dependence
at sufficiently high fields outside the AFM phase, but it deviates from
linearity at $T \le T_{\mathrm{N}}(0)$ and in
Yb(Rh$_{0.93}$Co$_{0.07}$)$_{2}$Si$_{2}$ it changes slope clearly inside the
AFM phase. Moreover, the FWHM of the fit function depends linearly on
temperature outside the phase, but remains constant inside, suggesting either
that such an analysis is valid only for $T \ge T_{\mathrm{N}}(0)$ or that the
Fermi surface changes continuously at $T = 0$ inside the AFM phase.}}
