Ivan Rodriguez had the most games by a catcher with 4+ hits, with 43 games.

Interpreted as:

catcher with most 4 or more hit regular-season game in career

	NAME	G	H	AB	R	2B	3B	HR	RBI	BB	HBP	SO	SB	CS	PA	TB	XBH	SH	SF	IBB	GIDP	AVG	OBP	SLG	OPS
1	Ivan Rodriguez I. Rodriguez	43	174	211	67	31	1	15	79	5	0	8	4	4	217	252	47	0	1	1	0	.825	.825	1.194	2.019
2	Bill Dickey B. Dickey	36	146	181	60	23	6	17	87	8	0	3	2		189	232	46	0			0	.807	.815	1.282	2.097
3	Mickey Cochrane M. Cochrane	27	110	133	57	19	6	12	58	10	0	2	2		143	177	37	0				.827	.839	1.331	2.170
4	Mike Piazza M. Piazza	26	106	123	48	17	0	22	69	11	0	2	1	1	134	189	39	0	0	2	0	.862	.873	1.537	2.410
5	Gabby Hartnett G. Hartnett	25	102	123	42	25	4	11	64	7	0	4	0		131	168	40	1			0	.829	.838	1.366	2.204
6	Ernie Lombardi E. Lombardi	24	103	119	34	20	2	5	50	1	0	1	0		120	142	27	0			1	.866	.867	1.193	2.060
7	A.J. Pierzynski	22	90	109	30	17	2	8	37	2	0	4	1	0	112	135	27	0	1	0	2	.826	.821	1.239	2.060
8	Ted Simmons T. Simmons	21	84	100	35	16	1	8	33	5	0	1	0	1	105	126	25	0	0	1	3	.840	.848	1.260	2.108
9	Smoky Burgess S. Burgess	21	87	101	35	15	3	11	43	7	0	0	0	1	108	141	29	0	0	1	0	.861	.870	1.396	2.266
10	Joe Mauer J. Mauer	20	85	106	34	17	2	7	54	4	0	4	3	0	111	127	26	0	1	2	1	.802	.802	1.198	2.000
11	Yadier Molina Y. Molina	19	76	93	26	12	1	6	41	3	0	2	1	1	96	108	19	0	0	1	1	.817	.823	1.161	1.984
12	Jason Kendall J. Kendall	18	73	85	25	18	1	2	18	3	1	3	6	1	89	99	21	0	0	0	1	.859	.865	1.165	2.030
13	Buster Posey B. Posey	17	70	87	25	17	1	7	29	2	0	5	1	1	89	110	25	0	0	0	1	.805	.809	1.264	2.073
14	Bengie Molina B. Molina	17	68	77	24	15	2	9	36	1	0	3	1	0	78	114	26	0	0	0	0	.883	.885	1.481	2.365
15	Jorge Posada J. Posada	17	68	83	30	18	0	11	41	2	0	6	0	0	85	119	29	0	0	1	3	.819	.824	1.434	2.257
16	Thurman Munson T. Munson	17	68	79	26	12	2	7	30	3	0	1	2	1	82	105	21	0	0	1	1	.861	.866	1.329	2.195
17	Gary Carter G. Carter	16	66	78	27	11	1	6	26	4	0	3	0	1	82	97	18	0	0	0	2	.846	.854	1.244	2.097
18	Luke Sewell L. Sewell	15	63	78	21	7	1	2	30	1	0	2	0		80	78	10	1				.808	.810	1.000	1.810
19	Lance Parrish L. Parrish	14	56	67	28	11	0	11	31	4	0	4	2	0	71	100	22	0	0	2	0	.836	.845	1.493	2.338
20	Manny Sanguillen M. Sanguillen	14	58	68	20	9	0	1	14	2	0	3	0	1	70	70	10	0	0	0	1	.853	.857	1.029	1.887
21	Sherm Lollar S. Lollar	14	57	69	20	5	1	5	24	1	1	0	0	0	71	79	11	0	0	0	1	.826	.831	1.145	1.976
22	Yogi Berra Y. Berra	14	57	69	21	14	3	8	42	3	0	1	1	0	72	101	25	0	0	0	0	.826	.833	1.464	2.297
23	Walker Cooper W. Cooper	14	59	66	25	7	1	11	37	2	1	1	2	0	69	101	19	0			1	.894	.899	1.530	2.429
24	Rick Ferrell R. Ferrell	14	56	69	20	15	2	1	28	2	1	0	2		73	78	18	1			0	.812	.819	1.130	1.950
25	Joe Girardi J. Girardi	13	52	63	19	9	1	2	34	1	0	1	1	0	65	69	12	0	1	0	1	.825	.815	1.095	1.911