Big Red Machine MVPs.

1970-1977 Cincinnati Reds were awarded the NL MVP six times in eight years: Bench, Bench, Rose, Morgan, Morgan, Foster.

New York Yankees won 6 of 8 1950-1957: Rizzuto, Berra, Berra, Berra, Mantle, Mantle.  The Yankees followed that two years later with four straight: Maris, Maris, Mantle, Howard.  Yanks won 10 of 14 1950-1963.  The only Reds to be MVP after 1977 were Barry Larkin in 1995 and Joey Votto in 2010.

But it may have been twice as hard to win MVP starting in 1969 when the leagues split into two divisions, creating two first place teams.  The Reds won the championship in 1975 and 1976; Morgan was MVP both years.

The same Reds started in 1975 and 1976.  1975 stats from baseball-reference.com:

Rk	Pos	Name	Age	G	PA	AB	R	H	2B	3B	HR	RBI	SB	CS	BB	SO	BA	OBP	SLG	OPS	OPS+	TB	GDP	HBP	SH	SF	IBB
1	C	Johnny Bench	27	142	606	530	83	150	39	1	28	110	11	0	65	108	.283	.359	.519	.878	140	275	12	2	0	8	12
2	1B	Tony Perez	33	137	574	511	74	144	28	3	20	109	1	2	54	101	.282	.350	.466	.816	124	238	12	3	0	6	6
3	2B	Joe Morgan*	31	146	639	498	107	163	27	6	17	94	67	10	132	52	.327	.466	.508	.974	169	253	3	3	0	6	3
4	SS	Dave Concepcion	27	140	558	507	62	139	23	1	5	49	33	6	39	51	.274	.326	.353	.679	87	179	17	2	6	4	4
5	3B	Pete Rose#	34	162	764	662	112	210	47	4	7	74	0	1	89	50	.317	.406	.432	.838	132	286	13	11	1	1	8
6	LF	George Foster	26	134	511	463	71	139	24	4	23	78	2	1	40	73	.300	.356	.518	.875	139	240	14	3	0	5	11
7	CF	Cesar Geronimo*	27	148	557	501	69	129	25	5	6	53	13	5	48	97	.257	.327	.363	.690	90	182	7	4	3	1	8
8	RF	Ken Griffey*	25	132	540	463	95	141	15	9	4	46	16	7	67	67	.305	.391	.402	.793	119	186	10	1	6	3	2