The original 16800A series logic analyzers had eight models:
16801A 34 logic analyzer channels, single slot
16802A 68 logic analyzer channels, single slot
16803A 102 logic analyzer channels, single slot
16804A 136 logic analyzer channels, dual slot
16806A 204 logic analyzer channels, dual slot
16821A 34 logic analyzer channels, 48 pattern generator channels, dual slot
16822A 68 logic analyzer channels, 48 pattern generator channels, dual slot
16823A 102 logic analyzer channels, 48 pattern generator channels, dual slot
The 34, 68, and 136 logic analyzer channel models used either one or two 16911A equivalent modules.
The 102 and 204 logic analyzer channel models used either one or two 16910A equivalent modules.
The 48 pattern generator channel models used a 16720A equivalent module.
The mainframes were equivalent to the two slot 16901A mainframe, except that the single slot 16800A models were cost reduced with lower capacity power supplies and a single module slot backplane. As far as I know a two slot 16800A mainframe is identical to a 16901A, except for mainframe ID information stored somewhere that the analyzer software can use to determine the mainframe type.
Also as far as I know the 16910A, 16911A, and 16720A equivalent modules used by the 16800A series are identical with normal 16910A, 16911A, and 16720A modules except for ID information stored somewhere that the analyzer software can use to determine the 16800 series specific module type.
I have never had a 16800A series logic analyzer myself to experiment with. As far as I know the ID information in the 16800A series mainframes and modules is used to lock the series so that logic analyzer and pattern generator modules cannot be interchanged between the 16800A series and the 16900A series. The logic analyzer software does not recognize modules swapped between the two series (again, I haven't verified that myself). That was probably just a marketing decision so that if you wanted complete flexibility in that form factor you would have to buy a 16901A mainframe at some price premium over a similarly configured 16800A series mainframe.
So anyway, back to the original question about upgrading a 68 channel 16802A with 4M sample depth, the analyzer module is equivalent to a 16911A. Those have 1M, 4M, 16M and 32M sample depth options, and 250 MHz and 500 MHz state options, and they are upgraded with a software license mechanism. When the upgrade license is installed on the module it must change something in non-volatile memory somewhere on the module. I am not aware of anyone yet who has successfully reverse engineered the 16910A / 16911A module option mechanism, so no one here can help you unless someone comes forward with new information about this.
If the 16800A series mainframes and modules weren't ID locked, one option would be to swap the analyzer module with a 32M sample depth 16752A or 16752B module. That would work on a 16900A series mainframe, but as far as I know would be prevented from working on a 16800A series mainframe. If that is incorrect, I would be happy to be corrected by someone who has tried it and found that it actually works.