Sorry, "continuation" was a little vague. We're specifically referring to "Natural Parameter Continuation"; but HB can also work with .STEP analysis.
There's an example of direct continuation in the Test Suite (source stepping in this case): Xyce_Regression/Netlists/Certification_Tests/BUG_573_SON
.global_param source_fac=0.1
.print HB V(Ve) V(out)
.print homotopy V(Vcc) V(1)
.hb 1MEG
.options hbint numfreq=50
.options linsol-hb type=belos
.options nonlin-hb continuation=1
.options loca stepper=0 predictor=0 stepcontrol=0
+ conparam=source_fac
+ initialvalue=0.1 minvalue=0.0 maxvalue=1
+ initialstepsize=0.1 minstepsize=1.0e-6 maxstepsize=0.3
+ aggressiveness=1
+ maxsteps=80 maxnliters=50
.op
R5 0 OUT 1MEG
V1 1 0 sin 0 {source_fac*1} 1meg AC 1
V2 Vcc 0 {source_fac*12}
C2 Vc OUT 10u
R4 0 Ve 270
R3 Vc Vcc 1.5k
Q1 Vc Vb Ve 2N2222
.MODEL 2N2222 NPN (Is=14.34f Xti=3 Eg=1.11 Vaf=74.03 Bf=255.9 Ne=1.307
+ Ise=14.34f Ikf=.2847 Xtb=1.5 Br=6.092 Nc=2 Isc=0 Ikr=0 Rc=1 Cjc=7.306p
+ Mjc=.3416 Vjc=.75 Fc=.5 Cje=22.01p Mje=.377 Vje=.75 Tr=46.91n Tf=411.1p
+ Itf=.6 Vtf=1.7 Xtf=3 Rb=10)
R2 0 Vb 6.8k
R1 Vb Vcc 39k
C1 1 Vb 10u
.end
If you're curious, an example of HB and .STEP is also in the test suite: Xyce_Regression/Netlists/Certification_Tests/BUG_340